On a class of generalized \(q\)-Bernoulli and \(q\)-Euler polynomials

DOI10.1186/1687-1847-2013-115zbMath1380.11019arXiv1201.6633OpenAlexW2141749442WikidataQ59292759 ScholiaQ59292759MaRDI QIDQ1693521

Nazim Idris Mahmudov, Marzieh Eini Keleshteri

Publication date: 31 January 2018

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

Full work available at URL: https://arxiv.org/abs/1201.6633

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Bernoulli and Euler numbers and polynomials (11B68)

Related Items

Determinant forms, difference equations and zeros of the \(q\)-Hermite-Appell polynomials ⋮ A study on \(q\)-Appell polynomials from determinantal point of view ⋮ Unnamed Item ⋮ On $q$-hypergeometric Bernoulli polynomials and numbers ⋮ An extended generalized \(q\)-extensions for the Apostol type polynomials ⋮ \(\lambda\)-\(q\)-Sheffer sequence and its applications ⋮ On a class of \(q\)-Bernoulli, \(q\)-Euler, and \(q\)-Genocchi polynomials ⋮ \(q\)-Bernoulli polynomials and \(q\)-umbral calculus ⋮ A novel approach for obtaining new identities for the lambda extension of q-Euler polynomials arising from the q-umbral calculus ⋮ \(q\)-difference equations for the 2-iterated \(q\)-Appell and mixed type \(q\)-Appell polynomials ⋮ Some identities on the generalized \(q\)-Bernoulli, \(q\)-Euler, and \(q\)-Genocchi polynomials ⋮ Some (p, q)-analogues of Apostol type numbers and polynomials ⋮ A general class of the three-variable unified Apostol-type \(q\)-polynomials and multiple power \(q\)-sums ⋮ A determinant approach to \(q\)-Bessel polynomials and applications ⋮ \(q\)-extensions for the Apostol type polynomials ⋮ A class of big (p,q)-Appell polynomials and their associated difference equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(q\)-extensions of some relationships between the Bernoulli and Euler polynomials
• A new class of generalized Apostol-Bernoulli polynomials and some analogues of the Srivastava-Pintér addition theorem
• \(q\)-analogues of the Bernoulli and Genocchi polynomials and the Srivastava-Pintér addition theorems
• Some new classes of generalized Apostol-Euler and Apostol-Genocchi polynomials
• Carlitz's \(q\)-Bernoulli and \(q\)-Euler numbers and polynomials and a class of generalized \(q\)-Hurwitz zeta functions
• Expansions of \(q\)-Bernoulli numbers
• \(q\)-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
• \(q\)-generalized Euler numbers and polynomials
• Some \(q\)-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order \(n\), and the multiple Hurwitz zeta function
• On \((i,q)\) Bernoulli and Euler numbers
• A new extension of \(q\)-Euler numbers and polynomials related to their interpolation functions
• Some results for the \(q\)-Bernoulli and \(q\)-Euler polynomials
• On a class of \(q\)-Bernoulli and \(q\)-Euler polynomials
• Remarks on some relationships between the Bernoulli and Euler polynomials.
• \(q\)-analogue of twisted \(l\)-series and \(q\)-twisted Euler numbers
• Generalizations of the Bernoulli and Appell polynomials
• Some formulae for the \(q\)-Bernoulli and Euler polynomials of higher order
• A generalization of the Bernoulli polynomials
• \(q\)-Bernoulli numbers and polynomials
• q-EXTENSIONS OF GENOCCHI NUMBERS
• ON THE ANALOGS OF BERNOULLI AND EULER NUMBERS, RELATED IDENTITIES AND ZETA AND L-FUNCTIONS
• On the q-Extensions of the Bernoulli and Euler Numbers, Related Identities and Lerch Zeta Function
• q-Bernoulli and Eulerian Numbers