MULTI-POLY-BERNOULLI NUMBERS AND RELATED ZETA FUNCTIONS
From MaRDI portal
Publication:3119527
DOI10.1017/nmj.2017.16zbMath1453.11035arXiv1503.02156OpenAlexW2962754876MaRDI QIDQ3119527
Hirofumi Tsumura, Masanobu Kaneko
Publication date: 12 March 2019
Published in: Nagoya Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1503.02156
Bernoulli and Euler numbers and polynomials (11B68) Multiple Dirichlet series and zeta functions and multizeta values (11M32)
Related Items
Alternating double \(t\)-values and \(T\)-values ⋮ A generalized regularization theorem and Kawashima's relation for multiple zeta values ⋮ MULTIPLE ZETA FUNCTIONS OF KANEKO-TSUMURA TYPE AND THEIR VALUES AT POSITIVE INTEGERS ⋮ COMBINATORIAL PROOFS OF IDENTITIES FOR SPECIAL VALUES OF ARAKAWA-KANEKO MULTIPLE ZETA FUNCTIONS ⋮ Some results on multiple polylogarithm functions and alternating multiple zeta values ⋮ Some identities of degenerate multi-poly-Changhee polynomials and numbers ⋮ Parametric Arakawa-Kaneko zeta function and Kaneko-Tsumura \(\eta \)-function ⋮ On a duality formula for certain sums of values of poly-Bernoulli polynomials and its application ⋮ Zeta functions connecting multiple zeta values and poly-Bernoulli numbers ⋮ Interpolated multiple zeta functions of Arakawa-Kaneko type ⋮ Generalized Arakawa-Kaneko zeta functions ⋮ On Arakawa-Kaneko zeta-functions associated with \(\mathrm{GL}_2(\mathbb{C})\) and their functional relations ⋮ Multi-poly-Bernoulli numbers and polynomials with a \(q\) parameter ⋮ On poly-cosecant numbers ⋮ Explicit relations between multiple zeta values and related variants ⋮ Duality formulas for Arakawa-Kaneko zeta values and related variants ⋮ Analytic continuation of multi-variable Arakawa-Kaneko zeta function for positive indices and its values at positive integers ⋮ Recursion formulas for poly-Bernoulli numbers and their applications ⋮ A note on Arakawa-Kaneko zeta values and Kaneko-Tsumura \(\eta\)-values ⋮ Weighted sum formulas from shuffle products of multiple zeta-star values ⋮ Variants of multiple zeta values with even and odd summation indices
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Arakawa-Kaneko \(L\)-functions and generalized poly-Bernoulli polynomials
- On generalized poly-Bernoulli numbers and related \(L\)-functions
- Symmetries of Bernoulli polynomial series and Arakawa-Kaneko zeta functions
- Gauss hypergeometric functions, multiple polylogarithms, and multiple zeta values
- Multiple harmonic series
- A generalization of the duality and sum formulas on the multiple zeta values
- Multiple polylogarithms, cyclotomy and modular complexes
- Kontsevich's integral for the Homfly polynomial and relations between values of multiple zeta functions
- Poly-Bernoulli numbers
- On multiple \(L\)-values
- Special values of hyperlogarithms and linear difference schemes
- \(p\)-adic multiple zeta values. I: \(p\)-adic multiple polylogarithms and the \(p\)-adic KZ equation
- Relations for multiple zeta values and Mellin transforms of multiple polylogarithms
- Multiple polylogarithms and multi-poly-Bernoulli polynomials
- Analytic continuation of multiple zeta-functions and their values at non-positive integers
- ON MULTIPLE ZETA VALUES OF EXTREMAL HEIGHT
- POLYLOGARITHMS AND POLY-BERNOULLI POLYNOMIALS
- Elementary Dirichlet Series and Modular Forms
- Multiple zeta values, poly-Bernoulli numbers, and related zeta functions
- The Sum Formula for Multiple Zeta Values and Connection Problem of the Formal Knizhnik-Zamolodchikov Equation
- Bernoulli Numbers and Zeta Functions
- Derivation and double shuffle relations for multiple zeta values
- The Arakawa-Kaneko zeta function
