General convolution identities for Bernoulli and Euler polynomials

DOI10.1016/j.jmaa.2015.11.006zbMath1400.11063arXiv1408.5178OpenAlexW2963710387MaRDI QIDQ898866

Karl Dilcher, Christophe Vignat

Publication date: 21 December 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.5178

zbMATH Keywords

Bernoulli numbersEuler numbersBernoulli polynomialsEuler polynomialsconvolution identities

Mathematics Subject Classification ID

Umbral calculus (05A40) Bernoulli and Euler numbers and polynomials (11B68) Other special orthogonal polynomials and functions (33C47) Linear difference operators (47B39)

Related Items (16)

Some new formulas for the products of the Frobenius-Euler polynomials ⋮ Unnamed Item ⋮ A unified approach to higher order convolutions within a certain subset of Appell polynomials ⋮ Explicit expressions and integral representations for the Stirling numbers: a probabilistic approach ⋮ Matiyasevich-type identities for hypergeometric Bernoulli polynomials and poly-Bernoulli polynomials ⋮ Explicit expressions for higher order binomial convolutions of numerical sequences ⋮ Unnamed Item ⋮ Nonlinear Identities for Bernoulli and Euler Polynomials ⋮ An explicit form of the polynomial part of a restricted partition function ⋮ Convolutions of the bi-periodic Fibonacci numbers ⋮ Special values and integral representations for the Hurwitz-type Euler zeta functions ⋮ A probabilistic generalization of the Stirling numbers of the second kind ⋮ Unnamed Item ⋮ Closed form expressions for Appell polynomials ⋮ A two-variable Dirichlet series and its applications ⋮ Probabilistic Stirling numbers of the second kind and applications

Uses Software

• DLMF

Cites Work

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• Convolution identities for Bernoulli and Genocchi polynomials
• New identities involving Bernoulli and Euler polynomials
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• On Miki's identity for Bernoulli numbers
• Higher-order convolutions for Bernoulli and Euler polynomials
• Bernoulli number identities from quantum field theory and topological string theory
• Applications of the classical umbral calculus
• The Classical Umbral Calculus
• A Characterization of the Gamma Distribution
• Probability

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