Hyperharmonic zeta and eta functions via contour integral

Bernoulli and Euler numbers and polynomials (11B68) (zeta (s)) and (L(s, chi)) (11M06) Other Dirichlet series and zeta functions (11M41) Special sequences and polynomials (11B83) Evaluation of number-theoretic constants (11Y60) Analytic continuation of functions of one complex variable (30B40)

Cites Work

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Series representations for the Stieltjes constants
Euler sums of hyperharmonic numbers
A theorem for the closed-form evaluation of the first generalized Stieltjes constant at rational arguments and some related summations
Expansions of generalized Euler's constants into the series of polynomials in \(\pi^{- 2}\) and into the formal enveloping series with rational coefficients only
Dirichlet series related to the Riemann zeta function
Hyperharmonic series involving Hurwitz zeta function
A formula of S. Ramanujan
Note on Dr. \textit{Vacca}'s series for \(\gamma\).
Theory and computation of Euler sums of generalized hyperharmonic numbers
On the values of a certain Dirichlet series at rational integers
On evaluations of Euler-type sums of hyperharmonic numbers
On the Stieltjes constants and gamma functions with respect to alternating Hurwitz zeta functions
Laurent expansion of harmonic zeta functions
Certain integral representations of Stieltjes constants \({\gamma_n}\)
On some explicit evaluations of nonlinear Euler sums
Approximation by special values of harmonic zeta function and log-sine integrals
Euler sums of multiple hyperharmonic numbers
Hypergeometric summation representations of the Stieltjes constants
Asymptotic estimates for Stieltjes constants: a probabilistic approach
THE VALUES OF AN EULER SUM AT THE NEGATIVE INTEGERS AND A RELATION TO A CERTAIN CONVOLUTION OF BERNOULLI NUMBERS
Alternating Euler sums at the negative integers
Computing Stieltjes constants using complex integration
The Power Series Coefficients of ξ(s)
On the Hurwitz zeta-function
On the Stieltjes constants with respect to harmonic zeta functions
On some formulae related to Euler sums
Stieltjes constants appearing in the Laurent expansion of the hyperharmonic zeta function
Euler sums of generalized harmonic numbers and connected extensions

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