Notes on generalization of the Bernoulli type polynomials

DOI10.1016/j.amc.2011.03.086zbMath1269.11023OpenAlexW2007702233MaRDI QIDQ648231

Burak Kurt, Yilmaz Simsek

Publication date: 22 November 2011

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2011.03.086

zbMATH Keywords

generating functionApostol-Bernoulli polynomialsBernoulli numbers and polynomialsEuler polynomialsApostol-Euler polynomialsApostol-Bernoulli polynomials of order \(\alpha \)consecutive sumsHurwitz-Lerch zeta functions

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Hurwitz and Lerch zeta functions (11M35)

Related Items (10)

A new class of generalized polynomials associated with Hermite and Euler polynomials ⋮ Euler basis, identities, and their applications ⋮ Bernoulli basis and the product of several Bernoulli polynomials ⋮ Unnamed Item ⋮ A new class of generalized polynomials ⋮ Application of orthonormal Bernoulli polynomials for approximate solution of some Volterra integral equations ⋮ Generating functions for generalized Stirling type numbers, array type polynomials, Eulerian type polynomials and their applications ⋮ A new class of generalized polynomials involving Laguerre and Euler polynomials ⋮ A new class of generalized polynomials associated with Laguerre and Bernoulli polynomials ⋮ On degenerate Apostol-type polynomials and applications

Cites Work

• Unnamed Item
• A new generalization of the Bernoulli and related polynomials
• A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi polynomials
• Some new families of generalized Euler and Genocchi polynomials
• \(q\)-Bernoulli numbers and polynomials associated with multiple \(q\)-zeta functions and basic \(L\)-series
• Twisted \((h,q)\)-Bernoulli numbers and polynomials related to twisted \((h,q)\)-zeta function and \(L\)-function
• Generalizations of Bernoulli numbers and polynomials
• Generalizations of Euler numbers and polynomials
• Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials
• ON THE ANALOGS OF BERNOULLI AND EULER NUMBERS, RELATED IDENTITIES AND ZETA AND L-FUNCTIONS
• The multiplication formulas for the Apostol–Bernoulli and Apostol–Euler polynomials of higher order
• Some formulas for the Bernoulli and Euler polynomials at rational arguments

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