Remarks on Some Integrals and Series Involving the Stirling Numbers and ζ(n)
From MaRDI portal
Publication:4846120
DOI10.2307/2154819zbMath0828.11044OpenAlexW4244723466MaRDI QIDQ4846120
Publication date: 21 August 1995
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/2154819
Riemann zeta functionidentitiesStirling numbers of the first kindgamma functionshypergeometric series with complex parameters
Bell and Stirling numbers (11B73) (zeta (s)) and (L(s, chi)) (11M06) Gamma, beta and polygamma functions (33B15) Zeta and (L)-functions: analytic theory (11M99)
Related Items (24)
Harmonic number identities via hypergeometric series and Bell polynomials ⋮ A note on some constants related to the zeta-function and their relationship with the Gregory coefficients ⋮ Parametric binomial sums involving harmonic numbers ⋮ Two series expansions for the logarithm of the gamma function involving Stirling numbers and containing only rational coefficients for certain arguments related to \(\pi^{-1}\) ⋮ Three open problems and a conjecture ⋮ Explicit evaluation of Euler and related sums ⋮ Further summation formulae related to generalized harmonic numbers ⋮ Infinite summation formulas related to Riemann Zeta function from hypergeometric series ⋮ Euler sums and Stirling sums ⋮ Explicit formulas of Euler sums via multiple zeta values ⋮ Some summation formulas involving harmonic numbers and generalized harmonic numbers ⋮ In the shadow of Euler's greatness: adventures in the rediscovery of an intriguing sum ⋮ Generalized harmonic numbers and Euler sums ⋮ Certain summation formulas involving harmonic numbers and generalized harmonic numbers ⋮ Summation formulas involving binomial coefficients, harmonic numbers, and generalized harmonic numbers ⋮ Identities for the Riemann zeta function ⋮ Expansions of generalized Euler's constants into the series of polynomials in \(\pi^{- 2}\) and into the formal enveloping series with rational coefficients only ⋮ Explicit evaluation of some quadratic Euler-type sums containing double-index harmonic numbers ⋮ On some combinatorial identities and harmonic sums ⋮ Infinite Summation Formulas Involving Riemann-Zeta function ⋮ Explicit evaluations of some families of log-sine and log-cosine integrals ⋮ 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: Remarks on Some Integrals and Series Involving the Stirling Numbers and ζ(n)
