The Arakawa-Kaneko zeta function
From MaRDI portal
Publication:5962076
DOI10.1007/s11139-009-9205-xzbMath1230.11106OpenAlexW2051211780MaRDI QIDQ5962076
Marc-Antoine Coppo, Bernard Candelpergher
Publication date: 16 September 2010
Published in: The Ramanujan Journal (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11139-009-9205-x
Bernoulli and Euler numbers and polynomials (11B68) Other Dirichlet series and zeta functions (11M41) Hurwitz and Lerch zeta functions (11M35) Multiple Dirichlet series and zeta functions and multizeta values (11M32)
Related Items (49)
Incomplete poly-Cauchy numbers ⋮ Poly-Cauchy numbers with a \(q\) parameter ⋮ Poly-Bernoulli numbers and polynomials with a \(q\) parameter ⋮ Some results on multiple polylogarithm functions and alternating multiple zeta values ⋮ Lonesum decomposable matrices ⋮ Euler sums and Stirling sums ⋮ Explicit formulas of Euler sums via multiple zeta values ⋮ Polylogarithmic zeta functions and their p-adic analogues ⋮ Combinatorial aspects of poly-Bernoulli polynomials and poly-Euler numbers ⋮ Multiple polylogarithms and multi-poly-Bernoulli polynomials ⋮ \(q\)-poly-Bernoulli numbers and \(q\)-poly-Cauchy numbers with a parameter by Jackson's integrals ⋮ Generalizations of poly-Bernoulli and poly-Cauchy numbers ⋮ A new class of identities involving Cauchy numbers, harmonic numbers and zeta values ⋮ Generalized incomplete poly-Bernoulli polynomials and generalized incomplete poly-Cauchy polynomials ⋮ Generalized harmonic numbers and Euler sums ⋮ Generalized harmonic number sums and quasisymmetric functions ⋮ On generalized Arakawa-Kaneko zeta functions with parameters \(a\), \(b\), \(c\) ⋮ On generalized poly-Bernoulli numbers and related \(L\)-functions ⋮ On a duality formula for certain sums of values of poly-Bernoulli polynomials and its application ⋮ Absolute series for higher Euler constants ⋮ Generalized Arakawa-Kaneko zeta functions ⋮ Poly-Euler polynomials and Arakawa-Kaneko type zeta functions ⋮ Explicit formula for generalization of poly-Bernoulli numbers and polynomials with a,b,c parameters ⋮ More properties on multi-poly-Euler polynomials ⋮ On Arakawa-Kaneko zeta-functions associated with \(\mathrm{GL}_2(\mathbb{C})\) and their functional relations ⋮ Harmonic-number summation identities, symmetric functions, and multiple zeta values ⋮ Barnes' multiple Frobenius-Euler and poly-Bernoulli mixed-type polynomials ⋮ Duality relations among multiple series with three parameters ⋮ Sum formulas of multiple zeta values with arguments multiples of a common positive integer ⋮ Inverse binomial series and values of Arakawa-Kaneko zeta functions ⋮ Arakawa-Kaneko \(L\)-functions and generalized poly-Bernoulli polynomials ⋮ Shifted poly-Cauchy numbers ⋮ An asymptotic series for an integral ⋮ Sum formulas of multiple zeta values with selected arguments ⋮ Symmetries of Bernoulli polynomial series and Arakawa-Kaneko zeta functions ⋮ Explicit relations between multiple zeta values and related variants ⋮ Duality formulas for Arakawa-Kaneko zeta values and related variants ⋮ Explicit formulae for sums of products of Bernoulli polynomials, including poly-Bernoulli polynomials ⋮ On some combinatorial identities and harmonic sums ⋮ A note on harmonic number identities, Stirling series and multiple zeta values ⋮ Multi Poly-Bernoulli and Multi Poly-Euler Polynomials ⋮ Poly-\(p\)-Bernoulli polynomials and generalized Arakawa-Kaneko zeta function ⋮ MULTI-POLY-BERNOULLI NUMBERS AND RELATED ZETA FUNCTIONS ⋮ An extension of the Euler-Maclaurin quadrature formula using a parametric type of Bernoulli polynomials ⋮ Unnamed Item ⋮ Recursion formulas for poly-Bernoulli numbers and their applications ⋮ On the convolutions of sums of multiple zeta(-star) values of height one ⋮ The \(p\)-adic Arakawa-Kaneko zeta functions and \(p\)-adic Lerch transcendent ⋮ Weighted sum formulas from shuffle products of multiple zeta-star values
Cites Work
- Unnamed Item
- New expressions of Hasse and Hermite formulas for the Hurwitz zeta function
- A generalization of the duality and sum formulas on the multiple zeta values
- Poly-Bernoulli numbers
- Multiple zeta values, poly-Bernoulli numbers, and related zeta functions
- Sum Relations for Multiple Zeta Values
- A note on poly-Bernoulli numbers and multiple zeta values
This page was built for publication: The Arakawa-Kaneko zeta function
