Extended Zeilberger's algorithm for identities on Bernoulli and Euler polynomials

DOI10.1016/j.jnt.2009.01.026zbMath1183.11011arXiv0810.0438OpenAlexW2963173937MaRDI QIDQ1026880

William Y. C. Chen, Lisa Hui Sun

Publication date: 6 July 2009

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.0438

zbMATH Keywords

identitiesBernoulli and Euler polynomialsZeilberger's algorithm

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Bernoulli and Euler numbers and polynomials (11B68) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items (18)

Some convolution identities for Frobenius-Euler polynomials ⋮ Padé approximation and Apostol-Bernoulli and Apostol-Euler polynomials ⋮ Some open problems related to creative telescoping ⋮ Symmetric identity for polynomial sequences satisfying \(A^\prime_{n+1}(x) = (n + 1)A_n(x)\) ⋮ Recurrence for values of the zeta function ⋮ A higher-order convolution for Bernoulli polynomials of the second kind ⋮ The extended Zeilberger algorithm with parameters ⋮ Derivation of identities involving some special polynomials and numbers via generating functions with applications ⋮ Unnamed Item ⋮ On multiple zeta values of even arguments ⋮ Some identities for multiple zeta values ⋮ Combinatorial identities for Appell polynomials ⋮ Shortened recurrence relations for generalized Bernoulli numbers and polynomials ⋮ Formal residue and computer-assisted proofs of combinatorial identities ⋮ Identities for Bernoulli polynomials and Bernoulli numbers ⋮ Symmetric recurrence relations and binomial transforms ⋮ Identity for generalized Bernoulli polynomials ⋮ p-Bernoulli and geometric polynomials

Uses Software

• Stirling

Cites Work

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• Convolution identities and lacunary recurrences for Bernoulli numbers
• Computer-assisted proofs of special function identities related to Poisson integrals
• Theory of summation in finite terms
• The method of creative telescoping
• A relation between Bernoulli numbers
• Combinatorial identities in dual sequences
• Computer proofs of a new family of harmonic number identities.
• A recurrence formula for the Bernoulli numbers
• Sums of products of Bernoulli numbers
• Summation algorithms for Stirling number identities
• Plane partitions. VI: Stembridge's TSPP theorem
• Applications of the classical umbral calculus
• On the non-holonomic character of logarithms, powers, and the \(n\)th prime function
• Identities concerning Bernoulli and Euler polynomials
• A New Approach to Bernoulli Polynomials
• Convolutions on the Ring of p -Adic Integers

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