\(p\)-adic distribution of the unification of the Bernoulli, Euler and Genocchi polynomials

DOI10.1016/j.amc.2011.01.075zbMath1229.11038OpenAlexW1964066270MaRDI QIDQ648245

Hacer Ozden

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.2011.01.075

zbMATH Keywords

Bernoulli polynomials\(p\)-adic distributionEuler polynomials

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 (14)

\((\rho,q)\)-Volkenborn integration ⋮ On (ρ,q)-Euler numbers and polynomials associated with (ρ,q)-Volkenborn integrals ⋮ A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi polynomials ⋮ Euler basis, identities, and their applications ⋮ Bernoulli basis and the product of several Bernoulli polynomials ⋮ A new class of Laguerre-based generalized Apostol polynomials ⋮ Some identities of higher order Barnes-type \(q\)-Bernoulli polynomials and higher order Barnes-type \(q\)-Euler polynomials ⋮ Hermite polynomials and their applications associated with Bernoulli and Euler numbers ⋮ Some identities of Carlitz degenerate Bernoulli numbers and polynomials ⋮ A REVISIT TO NON-LINEAR DIFFERENTIAL EQUATIONS ASSOCIATED WITH GENOCCHI NUMBERS ⋮ Some applications of degenerate poly-Bernoulli numbers and polynomials ⋮ A note on the truncated-exponential based Apostol-type polynomials ⋮ On the three families of extended Laguerre-based Apostol-type polynomials ⋮ Barnes-type Daehee with \(\lambda\)-parameter and degenerate Euler mixed-type polynomials

Cites Work

• A new generalization of the Bernoulli and related polynomials
• Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials
• 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
• Twisted \((h,q)\)-Bernoulli numbers and polynomials related to twisted \((h,q)\)-zeta function and \(L\)-function
• Generating functions of the \((h,q)\) extension of twisted Euler polynomials and numbers
• A family of \(p\)-adic twisted interpolation functions associated with the modified Bernoulli numbers
• A new extension of \(q\)-Euler numbers and polynomials related to their interpolation functions
• On the unification of Bernoulli and Euler polynomials
• A new proof of certain formulas for p-adic L-functions
• On a \(q\)-analogue of the \(p\)-adic log gamma functions and related integrals
• On the Lerch zeta function
• ON THE ANALOGS OF BERNOULLI AND EULER NUMBERS, RELATED IDENTITIES AND ZETA AND L-FUNCTIONS
• Some formulas for the Bernoulli and Euler polynomials at rational arguments
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