Euler and his work on infinite series
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Publication:5446658
DOI10.1090/S0273-0979-07-01175-5zbMath1135.01010MaRDI QIDQ5446658
Publication date: 6 March 2008
Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)
History of mathematics in the 18th century (01A50) Abel, Borel and power series methods (40G10) Zeta and (L)-functions: analytic theory (11M99)
Related Items (20)
A Wilf–Zeilberger–Based Solution to the Basel Problem With Applications ⋮ Statistical properties of sites visited by independent random walks ⋮ A variation of multiple $L$-values arising from the spectral zeta function of the non-commutative harmonic oscillator ⋮ Summation Formulas of Euler–Maclaurin and Abel–Plana: Old and New Results and Applications ⋮ Beyond the Basel problem: Euler’s derivation of the general formula for ζ (2n) ⋮ Euler's formula for the zeta function at the positive even integers ⋮ A simple algorithm for expanding a power series as a continued fraction ⋮ Explicit results for Euler’s factorial series in arithmetic progressions under GRH ⋮ A new approach to the representation of trigonometric and hyperbolic functions by infinite products ⋮ Partial fraction expansion of the hypergeometric functions ⋮ On Rayleigh-type formulas for a non-local boundary value problem associated with an integral operator commuting with the Laplacian ⋮ A class of integrals on squares, cubes and hypercubes ⋮ A new proof of Euler's formula for ζ(2n) ⋮ On a general class of trigonometric functions and Fourier series† ⋮ New expressions of Hasse and Hermite formulas for the Hurwitz zeta function ⋮ Optimizing the Gaussian kernel function with the formulated kernel target alignment criterion for two-class pattern classification ⋮ Series Expansions for the First Passage Distribution of Wong–Pearson Jump-Diffusions ⋮ Euler's factorial series at algebraic integer points ⋮ An Alternative Form of the Functional Equation for Riemann's Zeta Function, II ⋮ Convergence analysis of the summation of the factorially divergent Euler series by Padé approximants and the delta transformation
Cites Work
- Notes on Euler's work on divergent factorial series and their associated continued fractions
- Euler's 1760 paper on divergent series
- Irrationalité d'au moins un des neuf nombres ζ(5), ζ(7),...,ζ(21)
- Linear meromorphic differential equations: A modern point of view
- Irrationality of infinitely many values of the zeta function at odd integers.
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