Some classes of infinite series associated with the Riemann zeta and polygamma functions and generalized harmonic numbers.
From MaRDI portal
Publication:1855812
DOI10.1016/S0096-3003(01)00172-2zbMath1070.11038OpenAlexW2041231231MaRDI QIDQ1855812
Themistocles M. Rassias, Hari M. Srivastava
Publication date: 28 January 2003
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/43987
(zeta (s)) and (L(s, chi)) (11M06) Gamma, beta and polygamma functions (33B15) Computational number theory (11Y99)
Related Items (38)
Some evaluations of parametric Euler type sums of harmonic numbers ⋮ Explicit evaluation of Euler and related sums ⋮ Inequalities for the inverses of the polygamma functions ⋮ Identities for Reciprocal Binomials ⋮ A novel proof of two partial fraction decompositions ⋮ Finite Hurwitz-Lerch functions ⋮ Ramanujan formula for the generalized Stirling approximation ⋮ Some extensions for the several combinatorial identities ⋮ Some analytic continuations of the Barnes zeta function in two and higher dimensions ⋮ Finite summation formulas involving binomial coefficients, harmonic numbers and generalized harmonic numbers ⋮ Euler sums and Stirling sums ⋮ Estimating the digamma and trigamma functions by completely monotonicity arguments ⋮ Generalized \(q\)-Stirling numbers and their interpolation functions ⋮ Explicit formulas of Euler sums via multiple zeta values ⋮ Some summation formulas involving harmonic numbers and generalized harmonic numbers ⋮ Identities on harmonic and \(q\)-harmonic number sums ⋮ Generalized harmonic numbers and Euler sums ⋮ Summation formulas involving binomial coefficients, harmonic numbers, and generalized harmonic numbers ⋮ Sums of quadratic half integer harmonic numbers of alternating type ⋮ Gauss's theorem and harmonic number summation formulae with certain mathematical constants ⋮ Identities for the Riemann zeta function ⋮ Several polynomials associated with the harmonic numbers ⋮ New families of alternating harmonic number sums ⋮ Analysis of Apostol-Type Numbers and Polynomials with Their Approximations and Asymptotic Behavior ⋮ Alternating cubic Euler sums with binomial squared terms ⋮ Multiple zeta values and Euler sums ⋮ Identities for the harmonic numbers and binomial coefficients ⋮ Series representations for some mathematical constants ⋮ On generalized harmonic number sums ⋮ New improvements of the Stirling formula ⋮ Efficient approximations of finite and infinite real alternating p -series ⋮ Some applications of the Gamma and polygamma functions involving convolutions of the Rayleigh functions, multiple Euler sums and log-sine integrals ⋮ Applications of Apostol-type numbers and polynomials: approach to techniques of computation algorithms in approximation and interpolation functions ⋮ Some certain classes of combinatorial numbers and polynomials attached to Dirichlet characters: their construction by \(p\)-adic integration and applications to probability distribution functions ⋮ Quadratic alternating harmonic number sums ⋮ A family of shifted harmonic sums ⋮ Identities for the shifted harmonic numbers and binomial coeffecients ⋮ Partial-fraction decomposition of a rational function and its application
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A certain family of infinite series associated with digamma functions
- A certain class of infinite sums associated with Digamma functions
- On some series containing \(\psi{}(x)-\psi{}(y)\) and \((\psi{}(x)- \psi{}(y))^ 2\) for certain values of \(x\) and \(y\)
- Double and triple summation expressions obtained using perturbation theory
- Some infinite series and functional relations that arose in the context of fractional calculus
- Fractional calculus and the sums of certain families of infinite series
- On an Intriguing Integral and Some Series Related to ζ(4)
- Remarks on Some Integrals and Series Involving the Stirling Numbers and ζ(n)
- A Simple Algorithm for the Evaluation of a Class of Generalized Hypergeometric Series
This page was built for publication: Some classes of infinite series associated with the Riemann zeta and polygamma functions and generalized harmonic numbers.