On an Intriguing Integral and Some Series Related to ζ(4)
From MaRDI portal
Publication:4844433
DOI10.2307/2160718zbMath0840.11036OpenAlexW4236589488MaRDI QIDQ4844433
Jonathan M. Borwein, David Borwein
Publication date: 1 July 1996
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: http://hdl.handle.net/1959.13/940441
Gamma, beta and polygamma functions (33B15) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Summability and absolute summability of Fourier and trigonometric series (42A24) Zeta and (L)-functions: analytic theory (11M99)
Related Items (44)
Series representations for special functions and mathematical constants ⋮ Explicit evaluation of Euler and related sums ⋮ Further summation formulae related to generalized harmonic numbers ⋮ Extension of the four Euler sums being linear with parameters and series involving the zeta functions ⋮ Sharp inequalities for the harmonic numbers ⋮ Infinite summation formulas related to Riemann Zeta function from hypergeometric series ⋮ Experimental Evaluation of Euler Sums ⋮ A \(q\)-Raabe formula and an integral of the fourth Jacobi theta function ⋮ Infinite series identities on harmonic numbers ⋮ Three Symmetric Double Series by Telescoping ⋮ Euler sums and Stirling sums ⋮ Dirichlet type extensions of Euler sums ⋮ Explicit formulas of Euler sums via multiple zeta values ⋮ Harmonically Weighted Processes ⋮ In the shadow of Euler's greatness: adventures in the rediscovery of an intriguing sum ⋮ Generalized harmonic number sums and quasisymmetric functions ⋮ On two congruences involving Franel numbers ⋮ On some log-cosine integrals related to \(\zeta(3), \zeta(4)\), and \(\zeta(6)\). ⋮ The Laplace transform of the digamma function: An integral due to Glasser, Manna and Oloa ⋮ Analytic computation of digamma function using some new identities ⋮ Summation formulas involving binomial coefficients, harmonic numbers, and generalized harmonic numbers ⋮ Reviving the quadratic series of Au-Yeung ⋮ Harmonic series with polygamma functions ⋮ Parallel integer relation detection: Techniques and applications ⋮ Renewal sequences and record chains related to multiple zeta sums ⋮ Infinite series containing generalized harmonic numbers ⋮ New properties of \(r\)-Stirling series ⋮ Harmonic-number summation identities, symmetric functions, and multiple zeta values ⋮ Binomial sums involving harmonic numbers ⋮ An elementary evaluation of an intriguing integral via Fourier series ⋮ Multiple zeta values and Euler sums ⋮ On one-dimensional digamma and polygamma series related to the evaluation of Feynman diagrams ⋮ Integrals of polylogarithmic functions, recurrence relations, and associated Euler sums ⋮ Series representations for some mathematical constants ⋮ Unnamed Item ⋮ Four parametric linear Euler sums ⋮ New interesting Euler sums ⋮ Explicit evaluation of some quadratic Euler-type sums containing double-index harmonic numbers ⋮ Infinite Summation Formulas Involving Riemann-Zeta function ⋮ Arithmetic theory of harmonic numbers ⋮ Dixon's \(_3F_2(1)\)-series and identities involving harmonic numbers and the Riemann zeta function ⋮ Hyperharmonic series involving Hurwitz zeta function ⋮ Summing one- and two-dimensional series related to the Euler series ⋮ Some classes of infinite series associated with the Riemann zeta and polygamma functions and generalized harmonic numbers.
This page was built for publication: On an Intriguing Integral and Some Series Related to ζ(4)