J. W. L. Glaisher

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Person:1444254

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zbMath Open glaisher.j-w-lWikidataQ1356782 ScholiaQ1356782MaRDI QIDQ1444254

List of research outcomes

PublicationDate of PublicationType
https://portal.mardi4nfdi.de/entity/Q55154601966-01-01Paper
https://portal.mardi4nfdi.de/entity/Q58347571940-01-01Paper
On the improvements in algebraical notation made by Stifel, with an account of some of the notations used by the early algebraists.1927-01-01Paper
On division in algebra by a binomial or multinomial surd.1927-01-01Paper
Notes on the early history of the society.1926-01-01Paper
Partitionment of numbers in arithmetical progression into two parts \(\alpha\) and \(\beta\) such that \(\lambda\alpha + \mu\beta\) is equal to one of the numbers.1925-01-01Paper
On an indeterminate problem in Rudolff's algebra of 1525 and other indeterminate problems suggested by it.1925-01-01Paper
Partitionment of numbers in arithmetical progression into two parts \(\alpha\) and \(\beta\) such that \(\lambda \alpha+\mu \beta\) is equal to one of the numbers.1924-01-01Paper
On certain puzzle-questions occurring in early arithmetical writings and the general partition problems with which they are connected.1923-01-01Paper
On the early history of the signs \(+\) and \(-\) and on the early german arithmeticians.1921-01-01Paper
On early tables of logarithms and the early history of logarithms.1918-01-01Paper
Table of binomial-theorem coefficients.1917-01-01Paper
On \textit{Brigg}s process for the repeated extract of square roots.1916-01-01Paper
On \textit{Briggs}'s process for the repeated extraction of square roots.1916-01-01Paper
On some methods of calculating logarithms without the use of series.1916-01-01Paper
The earliest use of the radix method for calculating logarithms, with historical notices relating to the contributions of \textit{Oughtred} and others to mathematical notation.1915-01-01Paper
Tables of \(1\pm 2^{-n}+3^{-n}\pm 4^{-n}\;\and\) c. and \(1+3^{- n}+5^{-n}+7^{-n}+\and\) c. to 32 places of decimals.1914-01-01Paper
On the coefficients in the expansions of \(\frac{\cos x}{\cos 2x}\) and \(\frac{\sin x}{\cos 2x}\).1914-01-01Paper
Relations connecting quantities of the form \(S_n =1 + 2^{-n} + 3^{-n} + 4^{-n} +\) etc.1914-01-01Paper
Relations connecting quantities of the form \(S_n=1+2^{-n}+3^{-n}+4^{-n}+\) etc.1914-01-01Paper
A reciprocal transformation of a class of tables of integers.1913-01-01Paper
On the last two figures in certain coefficients analogues to the \textit{Euler}ian numbers.1913-01-01Paper
Relations connecting sums of powers of reciprocals of numbers and similar relations concerning other summations.1913-01-01Paper
On \textit{Euler}ian numbers (formulae, residues, endfigures) with the values of the first twenty-seven.1913-01-01Paper
On certain transformations of \textit{Lejeune-Dirichlet's} in the theory of numbers and similar theorems.1912-01-01Paper
Formulae connected with the divisors of sequences of numbers and asymptotic formulae derived therefrom.1912-01-01Paper
On some asymptotic summations and averages relating to the divisors of numbers.1912-01-01Paper
On \(1^n(x-1)^m + 2^n(x-2)^m + \cdots + (x-1)^n \cdot 1^m\) and other similar series.1912-01-01Paper
Summations of certain numerical series.1912-01-01Paper
Numerical values of the series \[ \begin{multlined} 1-\frac 13 -\frac 15 +\frac 17 +\frac 19 -\frac{1}{11} -\frac{1}{13} + \cdots \\ \text{and } 1 + \frac{1}{3^2} - \frac{1}{5^2} -\frac{1}{7^2} + \frac{1}{9^2} +\frac{1}{11^2} - \frac{1}{13^2} - \dots. \end{multlined} \]1912-01-01Paper
Transformations of the series \[ 1 - \frac 1{3^2} + \frac 1{5^2} - \frac 1{7^2} + \frac 1{9^2} - \cdots. \]1912-01-01Paper
Numerical values of the series \[ 1 - \frac{1}{3^n} + \frac{1}{5^n} - \frac{1}{7^n} + \frac{1}{9^n} - \cdots. \]1912-01-01Paper
Numerical values of the series \[ 1 - \frac{1}{3^n} + \frac{1}{5^n} - \frac{1}{7^n} + \frac{1}{9^n} - \cdots. \]1912-01-01Paper
On a class of relations connecting any \(n\) consecutive Bernoullian functions.1911-01-01Paper
Bernoullian numbers and other coefficients expressed in terms of numbers of the form \(\Delta^m 0^n\).1910-01-01Paper
On Dr. \textit{Vacca}'s series for \(\gamma\).1910-01-01Paper
Formulae for the number of partitions of a number into the elements \(1, 2, 3,\ldots, n\) up to \(n = 9\).1910-01-01Paper
Expansion of \((e^x - a)^{-1}\) and derived formulae: also values of \(\left( \frac{d}{d\theta} \right)^n \text{tan\,} \theta\).1909-01-01Paper
On the sum of the powers of the primitive \(n^{\text{th}}\) roots of unity.1909-01-01Paper
On the number of partitions of a number into a given number of parts (continued).1908-01-01Paper
Formulae for partitions into given elements derived from Sylvester's theorem.1908-01-01Paper
On the number of partitions of a number into a given number of parts.1908-01-01Paper
Relations between the divisors of the first \(n\) natural numbers.1908-01-01Paper
List of tables of \(\int_0^x e^{t^2} dt\) and connected integrals and functions.1908-01-01Paper
On elliptic-function expansions in which the coefficients are powers of the complex numbers having \(n\) as norm.1907-01-01Paper
On the numbers of representations of a number as a sum of \(2r\) squares, where \(2r\) does not exceed eighteen.1907-01-01Paper
On the representations of a number as the sum of fourteen and sixteen squares.1906-01-01Paper
On the representations of a number as the sum of eighteen squares.1906-01-01Paper
On the representation of a number as the sum of two, four, six, eight, ten, and twelve squares.1906-01-01Paper
On the series \(1-\frac 1{3^2}+\frac 1{5^2}-\frac 1{7^2}+\frac 1{9^2}-\dotsm \) (Second paper).1906-01-01Paper
On series for \(\frac 1{\pi}\) and \(\frac 1{\pi^2}\) (continued).1905-01-01Paper
On the expansions of \(\int_0^1k^nF(\varphi )\,dk\) and \(\int_0^1k^nE(\varphi )\,dk\), \(F(\varphi )\) and \(E(\varphi )\) being the Legendrian elliptic integrals.1905-01-01Paper
On the integral \(\int_0^1k^nKdk\).1905-01-01Paper
Note on an expansion of \((1+x)^k\) in Legendrian coefficients.1905-01-01Paper
The arithmetical functions \(P(m), Q(m), \varOmega(m)\).1905-01-01Paper
On the series for \(\frac 1\pi\) and \(\frac 1{\pi^2}\).1905-01-01Paper
On the expansions of the elliptic and zetafunctions of \(\frac 23 K\) in powers of \(q\).1905-01-01Paper
On the elliptic and zeta-functions of \(\frac 23 K\).1905-01-01Paper
On the representations of a number as a sum of four squares, and on some allied arithmetical functions.1904-01-01Paper
On the angles of pedal triangles of a triangle and some arithmetical questions connected therewith.1904-01-01Paper
On the series \(1-\frac{1}{3^2}+\frac{1}{5^2}- \frac{1}{7^2}+\frac{1}{9^2}-\cdots\).1903-01-01Paper
On the series \(1-\frac{1}{3^4}+\frac{1}{5^4}- \frac{1}{7^4}+\frac{1}{9^4}-\cdots\).1903-01-01Paper
On the expressions for the number of classes of a negative determinant, and on the numbers of positives in the octants of \(P\).1902-01-01Paper
Methods of increasing the convergence of certain series of reciprocals.1902-01-01Paper
On a method of increasing the convergence of certain series for \(\pi,\pi^2\), etc.1902-01-01Paper
On the distribution of the numbers for which \((\frac sP)=1\), or \(-1\), in the octants, quadrants, \&c., of \(P\).1902-01-01Paper
Formulae derived from \textit{Gauss}'s sums, with application to the series connected with the number of classes of binary forms.1902-01-01Paper
On a method of increasing the convergence of certain series for \(\pi, \pi^2 \and c\).1902-01-01Paper
On series for \(k\pi /n\) and \( k\pi/ \sqrt n\) whose terms are the reciprocals of the natural numbers.1902-01-01Paper
On the relation of the Abelian to the Jacobian elliptic functions.1902-01-01Paper
On some asymptotic formulae relating to the divisors of numbers.1902-01-01Paper
A general congruence theorem relating to the Bernoullian function.1901-01-01Paper
On the residues of Bernoullian functions for a prime modulus, including as special cases the residues of the Bernoullian, Eulerian and \(J\)-numbers.1901-01-01Paper
Table of the excess of the number of \((3k+1)\)-divisors of a number over the number of \((3k+2)\)-divisors.1901-01-01Paper
Table of the excess of the number of \((8k+1)\)- and \((8k+3)\)-divisors of a number over the number of \((8k+5)\)- and \((8k+7)\)-divisors.1901-01-01Paper
A series for \(\pi/\sqrt{7}\).1901-01-01Paper
On series for \(n\pi/\sqrt{P}\).1901-01-01Paper
Note on the residues of the ratios of certain series of inverse powers of numbers in arithmetical progression.1900-01-01Paper
Residue of the product of \(p\) numbers in arithmetical progression, mod. \(p^2\) and \(p^3\).1900-01-01Paper
On the residues of the sums of products of the first \(p 1\) numbers, and their powers, to modulus \(p^2\) or \(p^3\).1900-01-01Paper
On the residues of \(r^{p 1}\) to modulus \(p^2\), \(p^3\) etc.1900-01-01Paper
Relations connected with die residues of \(r^{p 1}\) to modulus \(p^2\) and \(p^3\).1900-01-01Paper
On the residues of the sums of the inverse powers of numbers in arithmetical progression.1900-01-01Paper
A congruence theorem relating to Eulerian numbers and other coefficients.1900-01-01Paper
Congruences relating to the sums of products of the first \(n\) numbers and to other sums of products.1900-01-01Paper
Residues of binomial theorem coefficients with respect to \(p^3\).1900-01-01Paper
A congruence theorem relating to the Bernoullian numbers.1900-01-01Paper
On \(1^n(x-1)^n+2^n(x-2)^n+\cdots+(x-1)^n1^n\) and other similar series.1900-01-01Paper
On the values of the series \(x^n+(x-q)^n+(x-2q)^n+\cdots+r^n\) und \(x^n-(x-q)^n+(x-2q)^n-\cdots\pm r^n\).1900-01-01Paper
On the residue to modulus \(p\), of \[ 1 + \frac1{3^{2n}} + \frac1{5^{2n}} +\cdots+ \frac1{(p 2)^{2n}}. \ .]1900-01-01Paper
Fundamental theorems relating to the Bernoullian numbers. (Second paper.).1899-01-01Paper
On a congruence theorem relating to an extensive class of coefficients.1899-01-01Paper
On a set of coefficients analogous to the Eulerian numbers.1899-01-01Paper
Fundamental theorems relating to the Bernoullian numbers.1899-01-01Paper
On the residue of a binomial-theorem coefficient with respect to a prime modulus.1899-01-01Paper
On the residue with respect to \(p^{n+1}\) of a binomial-theorem coefficient divisible by \(p^n\).1899-01-01Paper
A congruence theorem relating to sums of binomial-theorem coefficients.1899-01-01Paper
On the sums of the series \(1^n+2^n+\cdots+x^n\) and \(1^n-2^n+\cdots\pm x^n\).1899-01-01Paper
Divisibility of the sum of the products of the first \(n\) numbers taken \(r\) together.1898-01-01Paper
Table of the values of \(\frac12\cdot\frac23\cdot\frac45\cdots\frac{x-1}x\), the denominators being the series of prime numbers.1898-01-01Paper
Note on a theorem relating to sums of even powers of the natural numbers.1898-01-01Paper
Classes of recurring formulae involving Bernoullian numbers.1898-01-01Paper
On the Bernoullian function.1898-01-01Paper
General summation-formulae in finite differences.1898-01-01Paper
General summation-formulae in finite differences.1898-01-01Paper
On the definite integrals connected with the Bernoullian function.1896-01-01Paper
Correction of an error in the paper on numerical products in Vol. XXIII.1895-01-01Paper
On series involving inverse powers of subeven and supereven numbers.1894-01-01Paper
On certain numerical products in which the exponents depend upon the numbers.1894-01-01Paper
On the constant which occurs in the formula for \(1^1.2^2.3^3\dots n^n\).1894-01-01Paper
Note on a relation connecting constants analogous to Euler's constant.1894-01-01Paper
Products and series involving prime numbers only.1894-01-01Paper
Expressions for gamma functions in terms of complete elliptic integrals.1894-01-01Paper
Summation of series in which the \(r^{\text{th}}\) term is the reciprocal of the product of the members of the \(r^{\text{th}}\) set of \(n\) consecutive terms in an arithmetical progression.1894-01-01Paper
Summation of series in which the \(r^{\text{th}}\) term is the reciprocal of the product of the members of the \(r^{\text{th}}\) set of \(n\) consecutive terms in an arithmetical progression.1894-01-01Paper
On a series involving inverse squares of prime numbers.1893-01-01Paper
On the series \(\frac12+\frac15-\frac17+\frac{1}{11}-\frac{1}{13}+\) etc.1893-01-01Paper
Note on Mr. Kleiber's functions \(K_i\) and \(G_i\).1893-01-01Paper
On certain series and definite integrals.1893-01-01Paper
Developments in powers of \(k'^2-k^2\).1893-01-01Paper
Values of integrals in terms of \(k^2\).1893-01-01Paper
Note on the law of frequency of prime numbers.1893-01-01Paper
On the connexion between recurring formulae involving sums of divisors and the corresponding formulae involving differences between sums of even and uneven divisors.1892-01-01Paper
Relations between the divisors of the first \(n\) numbers.1891-01-01Paper
Note on a recurring formula for \(\sigma(n)\).1891-01-01Paper
Expressions for the sum of the cubes of the divisors of a number in terms of partitions of inferior numbers.1891-01-01Paper
On the sums of the inverse powers of the prime numbers.1891-01-01Paper
Calculation of the hyperbolic logarithm of \(\pi\) to thirty decimal places. -- Addition to the paper.1891-01-01Paper
On the series \(\frac 1 2 + \frac 1 3 + \frac 1 5 + \frac 1 7 + \frac 1 {11} +\) etc.1891-01-01Paper
On the series \(\frac 1 3 - \frac 1 5 + \frac 1 7 + \frac 1 {11} - \frac 1 {13} - \cdots\).1891-01-01Paper
On the \(q\)-series derived from the elliptic and zeta functions of \(\frac 13K\) and \(\frac 14K\).1891-01-01Paper
Expressions for symmetrical functions of \(I,G,E\) in terms of \(q\).1891-01-01Paper
Recurring relations involving sums of powers of divisors. sum of divisors, elliptic series, Bernoulli numbers, powers of divisors, triangular numbers1890-01-01Paper
Note on the sums of even powers of even and uneven numbers.1890-01-01Paper
On the elliptic functions of \(\frac 13K\).1890-01-01Paper
On the function which denotes the excess of the number of divisors of a number which \(\equiv 1\text{(mod.\,}3)\), over the number which \(\equiv 2\text{(mod.\,}3)\).1890-01-01Paper
On the square of Euler's series.1890-01-01Paper
On the series in which the exponents of the powers are the pentagonal numbers.1890-01-01Paper
Theorem relating to sums of even powers of the natural numbers.1890-01-01Paper
Mathematics and physics. Opening address.1889-01-01Paper
Note on series whose coefficients involve powers of the Bernoullian numbers.1889-01-01Paper
Expansions of \(K,I,G,E\) in powers of \(k'^2 - k^2\).1889-01-01Paper
On the expansion of \(\frac GK, \frac KG, \frac IE\) etc., in ascending powers of \(k^2\).1889-01-01Paper
The method of quarter-squares.1889-01-01Paper
On the expansions of the theta functions in ascending powers of the argument.1889-01-01Paper
On expressions for the theta functions as definite integrals. (Second paper.)1889-01-01Paper
The method of quarter squares.1889-01-01Paper
The method of quarter squares.1889-01-01Paper
On the series which represent the twelve elliptic and the four Zeta functions.1888-01-01Paper
Expressions for \(\Theta(x)\) as a definite integral.1887-01-01Paper
On the transformation and developments of the twelve elliptic functions and the four Zeta-functions.1887-01-01Paper
The mathematical Tripos.1887-01-01Paper
On the deduction of the \(q\)-series for the elliptic functions from the \(q\)-products.1886-01-01Paper
On the process of squaring the \(q\)-series for \(k\varrho\text{\,sn\,}u\), \(k\varrho\text{\,cn\,}u\), \(\varrho\text{\,dn\,}u\).1886-01-01Paper
On the process of squaring the Zeta-function.1886-01-01Paper
Note on the functions \(Z(u), \varTheta(u), \varPi(u,a)\).1886-01-01Paper
On the coefficients in the \(q\)-series for \(\frac{\pi}{2K}\) and \(\frac{2G}{\pi}\).1886-01-01Paper
Formulae in elliptic functions.1886-01-01Paper
On the function \(\chi (n)\).1885-01-01Paper
On the representations of a number as the sum of four uneven squares and as the sum of two even and two uneven squares.1885-01-01Paper
On certain sums of products of quantities depending upon the divisors of a number.1885-01-01Paper
On the quantities \(K,E,J,G,K',E',J',G'\) in elliptic functions.1885-01-01Paper
On the Zeta-functions.1885-01-01Paper
On the expression for the complete elliptic integral of the second kind as a series proceeding by sines of multiples of the modular angle.1885-01-01Paper
On the square of the series in which the coefficients are the sums of the divisors of the exponents.1885-01-01Paper
On the function which denotes the difference between the number of \((4m+1)\)-divisors and the number of \((4m+3)\)-divisors of a number.1884-01-01Paper
On the sum of the divisors of a number.1884-01-01Paper
Note on a class of formulae derivated from \(q\)-series in elliptic functions.1884-01-01Paper
On the square of the series in which the coefficients are the sums of the divisors of the exponents.1884-01-01Paper
Henry John Stephen Smith.1884-01-01Paper
Applications of Möbius's theorem on the reversion of certain series.1884-01-01Paper
James Challis.1883-01-01Paper
Notice of H. J. S. Smith.1883-01-01Paper
Theorems relating to the sum of the uneven divisors of a number.1883-01-01Paper
Factor table for the sixth million containing the least factor of every number not divisible by two, three or five between five million and six million.1883-01-01Paper
Note on the compositions of a number as a sum of two or four uneven squares.1883-01-01Paper
A system of integrals involving elliptic functions.1883-01-01Paper
Note on some algebraical formulae connected with a system of \(q\)-series in elliptic functions.1883-01-01Paper
Note on the time descent down the arc of a vertical parabola.1883-01-01Paper
Calculation of the hyperbolic logarithm of \(\pi\).1883-01-01Paper
Tables of the exponential function.1883-01-01Paper
Expression for \(\text{arg\,sn\,}\alpha\) and \((\text{arg\,sn\,}\alpha)^2\) as definite integrals.1883-01-01Paper
On certain formulae in elliptic functions.1883-01-01Paper
A theorem in partitions.1882-01-01Paper
On certain definite integrals involving the exponential-integral.1882-01-01Paper
Formulae for the \(t^{\text{th}}\) integral of a Legendrian coefficient and of the logarithm-integral.1882-01-01Paper
Examples illustrative of Cayley's theory of singular solutions.1882-01-01Paper
Proof of the addition equation for elliptic integrals of the second kind by means of the \(q\)-series.1882-01-01Paper
On a theorem in elliptic functions.1882-01-01Paper
On a method of deriving formulae in elliptic functions.1882-01-01Paper
Note on elliptic functions.1882-01-01Paper
On a partial differential equation.1882-01-01Paper
A chapter in elliptic functions1881-01-01Paper
On some definite integrals expressible in terms of the first complete elliptic integral and of gamma functions.1881-01-01Paper
Note on certain symbolic operators and their application to the solution of certain partial differential equations.1881-01-01Paper
On the general analogy between the formulae of singly and doubly periodic functions.1881-01-01Paper
A System of differential formulae in elliptic functions.1881-01-01Paper
Formulae for the sn, cn, dn of \(u+v+w\).1881-01-01Paper
On the connexion between elliptic functions and spherical trigonometry.1881-01-01Paper
Algebraical proof of the fractional series for the cotangent and cosecant.1881-01-01Paper
On Riccati's equation and its transformation, and on some definite integrals which satisfy them.1881-01-01Paper
On the \(q\) series in elliptic functions.1881-01-01Paper
On Riccati's equation and its transformation, and on some definite integrals which satisfy them.1881-01-01Paper
On elliptic functions.1881-01-01Paper
On the deduction of trigonometrical from elliptic function formulae.1880-01-01Paper
On some elliptic function and trigonometrical theorems.1880-01-01Paper
A system of trigonometrical formulae.1880-01-01Paper
On the addition equation for the third elliptic integral.1880-01-01Paper
Note on a method of obtaining the \(q\)-formula for the sine-amplitude in elliptic functions.1880-01-01Paper
Theorem connected with a certain figure inscribed in a circle.1880-01-01Paper
Note on a trigonometrical identity involving products of four sines.1880-01-01Paper
On algebraical expansions of which the fractional series for the cotangent and cosecant are the limiting formes.1880-01-01Paper
Theorems in elementary trigonometry.1880-01-01Paper
Addition to a previous paper on some theorems in trigonometry.1880-01-01Paper
Trigonometrical theorems involving the products of four sines or four cosines.1880-01-01Paper
Note on an example in Boole's ``Differential equations relating to orthogonal trajectories.1880-01-01Paper
A trigonometric identity.1880-01-01Paper
On some identities in the theory of elliptic functions.1880-01-01Paper
Note on an expansion of Euler's.1880-01-01Paper
On Rodrigues' theorem.1880-01-01Paper
Theorem in elliptic functions.1880-01-01Paper
On some algebraical expressions which are unaltered by certain substitutions.1880-01-01Paper
Note on a point in the method of least squares.1880-01-01Paper
Systems of formulae in elliptic functions.1880-01-01Paper
A trigonometrical identity.1880-01-01Paper
On long successions of composite numbers.1880-01-01Paper
Theorem in partitions.1880-01-01Paper
On the method of least squares.1880-01-01Paper
Note on an algebraical identity.1880-01-01Paper
Addition to a paper: ``A theorem in trigonometry. Vol. XV. p. 151-157.1879-01-01Paper
On a space-locus connected with the ellipsoid.1879-01-01Paper
On a special form of determinants and on certain functions of \(n\) variables analogoues to the sine and cosine.1879-01-01Paper
An enumeration of prime pairs.1879-01-01Paper
Generalisation of Prof. Cayley's theorem on partition.1879-01-01Paper
On certain sums of squares.1879-01-01Paper
Value of a series.1879-01-01Paper
Example illustrative of a point in the solution of differential equations in series.1879-01-01Paper
On a class of algebraical identities.1879-01-01Paper
Note on Cayley's theorem.1879-01-01Paper
On Cauchy's theorem relating to the factors of \((x+y)^n-x^n-y^n\).1879-01-01Paper
On the caustic by refraction of a cercle for parallel rays.1879-01-01Paper
James Booth.1879-01-01Paper
Theorem in algebra.1879-01-01Paper
On a class of determinants, with a note on partition.1879-01-01Paper
Separate enumeration of primes of the form \(4n+1\) and of the form \(4n+3\).1879-01-01Paper
Addition to a paper on factor tables.1879-01-01Paper
Factor table for the fourth million. \(4^\circ\).1879-01-01Paper
On circulating decimals with special reference to Henry Goodwyn's ``Table of circles and ``Tabular series of decimal quotients. (London 1818-1823).1879-01-01Paper
On a property of vulgar fractions.1879-01-01Paper
Summation of a class of trigonometrical series.1879-01-01Paper
On a symbolic theorem involving repeated differentiations.1879-01-01Paper
On certain symbolic theorems of Prof. Crofton's.1879-01-01Paper
Certain symbolic theorems derived from Lagrange's series.1879-01-01Paper
Note on a formula in elliptic functions.1879-01-01Paper
A group of formulae connecting the elliptic functions of four quantities.1879-01-01Paper
Values of the Theta- and Zetafunctons for certain values of the argument.1879-01-01Paper
On definite integrals involving elliptic functions.1879-01-01Paper
Formulae in elliptic functions.1879-01-01Paper
Note on the above.1879-01-01Paper
On certain special enumeration of primes.1878-01-01Paper
On factor tables with an account of the mode of formation of the factor table for the fourth million.1878-01-01Paper
Generalised form of certain series.1878-01-01Paper
On the solution of a differential equation allied to Riccati's.1878-01-01Paper
On expressions for the theta-functions as definite integrals.1878-01-01Paper
Euler's formula in trigonometry.1878-01-01Paper
On the law of force to any point in the plane of motion in order that the orbit may be always a conic.1878-01-01Paper
On the law of force to any point when the orbite is a conic.1878-01-01Paper
On multiplication by a table of single entry.1878-01-01Paper
Solution of a question (5249).1878-01-01Paper
Note on calculating decimals.1878-01-01Paper
On the factors of a special form of determinants.1877-01-01Paper
On a class of determinants.1877-01-01Paper
Numerical value of a series.1877-01-01Paper
Theorems involving certain exponential symbolic operators.1877-01-01Paper
Note on certain theorems in definite integration.1877-01-01Paper
Note on Cauchy's theorem relating to the factors of \((x+y)^n-x^n-y^n\).1877-01-01Paper
On the value of a class of determinants.1877-01-01Paper
Preliminary account of an enumeration of the primes in Burckhardt's tables (1 to 3000000.)1877-01-01Paper
Theorem relating to the difference between the sums of the even and uneven divisors of a number.1877-01-01Paper
On some continued fractions.1877-01-01Paper
Note on the reversion of series of a certain form.1877-01-01Paper
Four algebraical theorems.1877-01-01Paper
On the numerical value of a certain series.1877-01-01Paper
On the product \(1^1.2^2.3^3\ldots n^n\).1877-01-01Paper
Further note on certain numerical continued products.1877-01-01Paper
Series and products for \(\pi\) and powers of \(\pi\).1877-01-01Paper
An approximate numerical theorem involving e and \(\pi\).1877-01-01Paper
On certain identical differential equations.1877-01-01Paper
Transformation of some definite integrals.1877-01-01Paper
Expansion derived of Lagrange's series.1877-01-01Paper
Numerical values of the first twelve powers of \(\pi\), of their reciprocals and of certain other related quantities.1877-01-01Paper
On a formula in elliptic functions.1877-01-01Paper
Arithmetical note.1877-01-01Paper
On long successions of composite numbers.1877-01-01Paper
Proof of Stirling's theorem \[ 1.2.3\ldots n=\sqrt{2n\pi}.n^ne^{-n}. \]1877-01-01Paper
Theorem of an exponential symbolical operator.1877-01-01Paper
On the enumeration of the primes in Burckhardt's and Dase tables.1877-01-01Paper
On long successions of composite numbers.1877-01-01Paper
Theorem in trigonometry.1877-01-01Paper
On certain determinants.1876-01-01Paper
Biographie de Jean Wilson.1876-01-01Paper
Theorem relating to the differentiation of a symmetrical determinant.1876-01-01Paper
On the representation of an uneven number as a sum of four squares and as the sum of a square and two triangular numbers.1876-01-01Paper
Note in regard to multiple differentiation.1876-01-01Paper
Further note in regard to a multiple differentiation of a certain expression.1876-01-01Paper
On a formula of Cauchy's for the evaluation of a class definite integrals.1876-01-01Paper
Values of certain infinite products, with an application to the summation of the geometrical series of the \(n^{\text{th}}\) order as a definite integral.1876-01-01Paper
On a series summation leading to an expression for the Thetafunction as a definite integral.1876-01-01Paper
Preliminary account of the results of an enumeration of the primes in Dase's tables (6,000,000 to 9,000,000).1876-01-01Paper
Solution of a question (4797).1876-01-01Paper
Note on Sylvester's paper: Development of an idea of Eisenstein. Quart. J. I. p.~199.1876-01-01Paper
Solution of a question (4512).1876-01-01Paper
On a class of identical relations in the theory of elliptic functions.1876-01-01Paper
On formulae of verification in the partition of numbers.1875-01-01Paper
Miscellaneous theorems.1875-01-01Paper
On a numerical continued product.1875-01-01Paper
Relation connecting the derivatives of \(e^{\surd x}\).1875-01-01Paper
On the integral \(\int_{0}^{\infty} \frac{\cos x}{a^2 + x^2}dx\).1875-01-01Paper
Expression for \(\theta (x)\) as a definite integral.1875-01-01Paper
Notes on certain formulae in Jacobi's Fundamenta Nova.1875-01-01Paper
On some elliptic function identitics.1875-01-01Paper
Expressions for Laplace's coefficients, Bernoullian and Eulerian numbers etc. as determinants.1875-01-01Paper
On Herwart ab Hohenburg's Tabulae Arithmeticae \(\pi\varrho o\sigma\theta\alpha\varphi\varepsilon\iota\varrho \varepsilon\sigma\acute\varepsilon\omega\zeta\) universales Munich 1610.1875-01-01Paper
On partition of numbers1875-01-01Paper
Theorems relating to the divisors of a number.1875-01-01Paper
Theorems in partitions.1875-01-01Paper
Arithmetical proof of Clausen's identity.1875-01-01Paper
Three theorems in arithmetic.1875-01-01Paper
Identities.1875-01-01Paper
On some algebraical formulae.1875-01-01Paper
Note on an integral.1875-01-01Paper
Proof of some theorems of Mr. Liouville on definite integrals.1875-01-01Paper
Notes on Laplace's coefficients.1875-01-01Paper
Solution of a question (4391).1875-01-01Paper
Note on the formula \[ 1^3 + 2^3 + \cdots + n^3 = (1 + 2 + \cdots + n)^2. \]1875-01-01Paper
On the integral \[ \int_0^\pi \left( \frac{\sin^2 x}{1 2a\cos x+a^2} \right)^m dx. \ .]1875-01-01Paper
Proof that \[ \int_{-\infty}^{\infty} \left( x-\frac ax \right) dx = \int_{-\infty}^{\infty} \varphi(x)dx. \]1875-01-01Paper
On a class of identical relations in the theory of elliptic functions.1875-01-01Paper
Solution of a question (4395).1875-01-01Paper
Bemerkung zum Problem (4298).1875-01-01Paper
Note on the foregoing paper.1875-01-01Paper
Note on Fourier's theorem.1875-01-01Paper
A theorem in arithmetic.1875-01-01Paper
Note on partitions.1875-01-01Paper
Values of certain infinite products.1875-01-01Paper
On an identity.1875-01-01Paper
On the \(n^{\text{th}}\) roots of unity.1874-01-01Paper
On the problem of the eight queens.1874-01-01Paper
On partitions and derivations.1874-01-01Paper
Note on pythagorean triangles (Question 4102).1874-01-01Paper
A pythagorean sieve.1874-01-01Paper
Numerical values of certain continued fractions.1874-01-01Paper
Note on continued fractions for tan \(nx\).1874-01-01Paper
On the integrals \[ \int_0^{\infty} \sin x^2 dx \text{ and } \int_0^{\infty} \cos x^2 dx. \]1874-01-01Paper
Proof of the formula \[ KE' + K'E - KK' = \frac \pi 2. \]1874-01-01Paper
Summation of selected terms of a series.1874-01-01Paper
Account of the method employed by Professors J. M. Rice and W. W. Johnson for obtaining the differentials of functions.1874-01-01Paper
A new formula in definite integrals.1874-01-01Paper
On some elliptic-transcendent relations.1874-01-01Paper
Verification of an elliptic transcendent identity.1874-01-01Paper
Account of a M. S. Table of twelve figure logarithms of numbers from 1 to 120000, calculated by the late Mr. John Thomson, of Greenock, and recently presented to the Royal Astronomical Society by his sister.1874-01-01Paper
On the transformation of continued products into continued fractions.1873-01-01Paper
A continued fraction for tan \(nx\).1873-01-01Paper
Note on a paper by Mr. Stone, ``On the rejection of discordant observations.1873-01-01Paper
Geometrical proof that \[ 1^3 +2^3 +3^3 \ldots +n^3 = (1+2+3 \ldots +n)^2. \]1873-01-01Paper
On the evaluation of a class of definite integrals involving circular functions in the numerator and powers of the variables in the denominator.1873-01-01Paper
On the solution of the equations in the method of least squares.1873-01-01Paper
Zur Behandlung der Proportionen im Zusammenhang mit der Verbesserung des geometrischen Lehrens.1873-01-01Paper
On the progress to accuracy of logarithmic tables.1873-01-01Paper
On the quadrature of the circle A. D. 1580-1630.1873-01-01Paper
Arithmetic irrationality.1873-01-01Paper
Note on a question in probabilities connected with the performance of calculations in duplicate.1873-01-01Paper
On the probability of errors of different amounts in calculations, attributable to the uncertainty of the last figure through contraction.1873-01-01Paper
On the rejection of discordant observations.1873-01-01Paper
Tables of the first 250 Bernoulli's numbers (to nine figures) and their logarithms (to ten figures).1873-01-01Paper
On the evaluation of a class of definite integrals involving circular functions in the numerator and powers of the variable only in the denominator.1873-01-01Paper
On the calculation of the theoretical unit-angle to a great number of decimal places.1873-01-01Paper
Generalisation of the foregoing theorem.1873-01-01Paper
Remarks on logarithmic and factor tables with special reference to Mr. Drach's suggestions.1873-01-01Paper
On logarithmic tables.1873-01-01Paper
Solution of question 3722.1873-01-01Paper
Solution of question 3600 (by W. Roberts).1873-01-01Paper
Solution of question 3539.1873-01-01Paper
Solution of question 3643.1873-01-01Paper
Solution of question 3599.1873-01-01Paper
On the relations between the particular integrals in Cayley's solution of Riccati's equation.1872-01-01Paper
On certain series for \(\pi\).1872-01-01Paper
Arithmetical identities.1872-01-01Paper
Simple proof of a known property of Bernoulli's numbers.1872-01-01Paper
On errors in Vlacq's (often called Brigg's or Neper's) table of ten-figure logarithms of numbers.1872-01-01Paper
Addition to a paper on errors in Vlacq's ten-figure logarithms published in the last number of the monthly notices.1872-01-01Paper
On the law of distribution of prime numbers.1872-01-01Paper
Remarks on certain portions of Laplace's proof of the method of least squares.1872-01-01Paper
On the law of facility of errors of observations and on the method of least squares.1872-01-01Paper
On semi-convergent series.1872-01-01Paper
On a deduction from von Staudt's property of Bernoulli's numbers.1872-01-01Paper
On the constants which occur in certain summations by Bernoulli's series.1872-01-01Paper
On functions with recurring derivatives.1872-01-01Paper
Solution of question 3520.1872-01-01Paper
Note on certain definite integrals.1872-01-01Paper
On the evaluation in series of certain definite integrals.1872-01-01Paper
On the function that stands in the same relation to Bernoulli's numbers that the Gamma-function does to fractionals.1872-01-01Paper
Solution of question 3429.1872-01-01Paper
On a differential equation allied to Riccati's.1872-01-01Paper
Values of certain infinite products.1872-01-01Paper
On the expression for \[ \varphi(x+yi)+\varphi(x-yi). \]1871-01-01Paper
Remarks on the calculation of \(\pi\).1871-01-01Paper
On the summation by definite integrals of the geometrical series of the second and higher orders.1871-01-01Paper
On the integrals \[ \int_0^{\infty}\sin (x^{n})dx\;\text{and}\;\int_0^{\infty}\cos (x^{n}) dx. \]1871-01-01Paper
Mathematical notes. 1) An arithmetical proposition.1871-01-01Paper
On the deduction of series from infinite products.1871-01-01Paper
Remarks on certain series occurring in a paper ``On the deduction of series from infinite products.1871-01-01Paper
Remarks on a theorem in Laplace's probabilities.1871-01-01Paper
On the reduction of functional transcendents.1871-01-01Paper
On Fourier's (double integral) theorem.1871-01-01Paper
Notes on definite integrals.1871-01-01Paper
Suggested notation for printing complicated exponents.1871-01-01Paper
On certain theorems in logarithmic transcendents.1871-01-01Paper
Pineto's table of ten-figure logarithms of numbers.1871-01-01Paper
Review of Mr. Sang's logarithms.1871-01-01Paper
On a paradox in infinite series.1871-01-01Paper
On the summation by definite integrals of the geometrical series of the second and higher orders.1871-01-01Paper
On the history of Euler's constant.1871-01-01Paper
On the calculation of Euler's constant.1871-01-01Paper
Note on the integral \(\int_0^{\infty}\frac{\cos bx}{a^{2} + x^{2}}dx\).1871-01-01Paper
On Riccati's equation.1871-01-01Paper
On Lambert's proof of the irrationality of \(\pi\) and on the irrationality of certain other quantities.1871-01-01Paper
Remarks on the calculation of \(\pi\).1871-01-01Paper
Tables of elliptic functions.1871-01-01Paper
On a class of definite integrals.1871-01-01Paper
Tables of the numerical values of the sine-integral, cosine-integral, and exponential-integral.1870-01-01Paper
On a theorem in definite integration.1870-01-01Paper
On \(\sin \infty\) and \(\cos \infty\).1869-01-01Paper

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