On generating functions for the special polynomials

DOI10.2298/FIL1701009SzbMath1488.11059OpenAlexW2602976799MaRDI QIDQ5005306

Yilmaz Simsek

Publication date: 9 August 2021

Published in: Filomat (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2298/fil1701009s

zbMATH Keywords

generating functionsEuler numbersApostol-Bernoulli polynomialsEuler polynomialsFrobenius-Euler numbersFrobenius-Euler polynomialsApostol-Bernoulli numbers

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80)

Related Items (5)

New integral formulas and identities involving special numbers and functions derived from certain class of special combinatorial sums ⋮ Analysis of generating functions for special words and numbers and algorithms for computation ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Computation of k-ary Lyndon words using generating functions and their differential equations

Cites Work

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• Generating functions for \(q\)-Apostol type Frobenius-Euler numbers and polynomials
• Some generalizations of the Apostol-Genocchi polynomials and the Stirling numbers of the second kind
• A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi polynomials
• Carlitz's \(q\)-Bernoulli and \(q\)-Euler numbers and polynomials and a class of generalized \(q\)-Hurwitz zeta functions
• \(q\)-Bernoulli numbers and polynomials associated with multiple \(q\)-zeta functions and basic \(L\)-series
• Some \(q\)-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order \(n\), and the multiple Hurwitz zeta function
• Some new identities for the Apostol-Bernoulli polynomials and the Apostol-Genocchi polynomials
• \(q\)-analogue of twisted \(l\)-series and \(q\)-twisted Euler numbers
• Generating functions for generalized Stirling type numbers, array type polynomials, Eulerian type polynomials and their applications

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