Higher-order Frobenius-Euler and poly-Bernoulli mixed-type polynomials

DOI10.1186/1687-1847-2013-251zbMath1375.11025arXiv1307.3062OpenAlexW2103745297WikidataQ59299222 ScholiaQ59299222MaRDI QIDQ1682146

Taekyun Kim, Dae San Kim

Publication date: 28 November 2017

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.3062

zbMATH Keywords

umbral calculuspoly-Bernoulli polynomialsFrobenius-Euler polynomialsmixed-type polynomials

Mathematics Subject Classification ID

Umbral calculus (05A40) Bernoulli and Euler numbers and polynomials (11B68) Special sequences and polynomials (11B83)

Related Items (13)

Barnes' multiple Bernoulli and generalized Barnes' multiple Frobenius-Euler mixed-type polynomials ⋮ Fully degenerate poly-Bernoulli numbers and polynomials ⋮ Barnes-type degenerate Euler polynomials ⋮ Some explicit formulas for the generalized Frobenius-Euler polynomials of higher order ⋮ Reciprocal relations of Bernoulli and Euler numbers/polynomials ⋮ A note on degenerate poly-Bernoulli numbers and polynomials ⋮ Explicit formula for generalization of poly-Bernoulli numbers and polynomials with a,b,c parameters ⋮ Revisit of identities for Apostol-Euler and Frobenius-Euler numbers arising from differential equation ⋮ A note on poly-Bernoulli numbers and polynomials of the second kind ⋮ Multi Poly-Bernoulli and Multi Poly-Euler Polynomials ⋮ Some applications of degenerate poly-Bernoulli numbers and polynomials ⋮ A new class of Hermite-Apostol type Frobenius-Euler polynomials and its applications ⋮ A generalization of power and alternating power sums to any Appell polynomials

Cites Work

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• Degenerate poly-Bernoulli polynomials with umbral calculus viewpoint
• Identities involving Frobenius-Euler polynomials arising from non-linear differential equations
• An identity of the symmetry for the Frobenius-Euler polynomials associated with the fermionic \(p\)-adic invariant \(q\)-integrals on \({\mathbf Z}_p\)
• Power series and asymptotic series associated with the \(q\)-analog of the two-variable \(p\)-adic \(L\)-function
• The umbral calculus
• On the generalized Apostol-type Frobenius-Euler polynomials
• A note on the Frobenius-Euler numbers and polynomials associated with Bernstein polynomials
• Exploring the multiple Changheeq-Bernoulli polynomials
• Twisted Dedekind Type Sums Associated with Barnes' Type Multiple Frobenius-Euler l-Functions

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