A note on degenerate Bernoulli numbers and polynomials associated with \(p\)-adic invariant integral on \(\mathbb{Z}_p\)

DOI10.1016/j.amc.2015.02.068zbMath1390.11049OpenAlexW2009760747MaRDI QIDQ1636834

Taekyun Kim, Dmitry V. Dolgy, Dae San Kim

Publication date: 7 June 2018

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

Full work available at URL: https://doi.org/10.1016/j.amc.2015.02.068

zbMATH Keywords

\(p\)-adic invariant integraldegenerate Bernoulli polynomial\(\lambda\)-Daehee polynomial

Mathematics Subject Classification ID

Umbral calculus (05A40) Exact enumeration problems, generating functions (05A15) Binomial coefficients; factorials; (q)-identities (11B65) Bernoulli and Euler numbers and polynomials (11B68) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80)

Related Items (14)

Degenerate poly-Cauchy polynomials with a \(q\) parameter ⋮ Degenerate poly-Bernoulli polynomials with umbral calculus viewpoint ⋮ On fully degenerate Daehee numbers and polynomials of the second kind ⋮ On finite-times degenerate Cauchy numbers and polynomials ⋮ Higher Order Degenerate Hermite-Bernoulli Polynomials Arising from $p$-Adic Integrals on $mathbb{Z}_p$ ⋮ On \(\lambda\)-linear functionals arising from \(p\)-adic integrals on \(\mathbb{Z}_p\) ⋮ Degenerate changhee-Genocchi numbers and polynomials ⋮ Fully degenerate Bernoulli numbers and polynomials ⋮ On $p$-adic integral for generalized degenerate Hermite-Bernoulli polynomials attached to $\chi$ of higher order ⋮ A note on the Barnes-type \(q\)-Euler polynomials ⋮ On degenerate Bell numbers and polynomials ⋮ Identities of the degenerate Daehee numbers with the Bernoulli numbers of the second kind arising from nonlinear differential equation ⋮ Degenerate, partially degenerate and totally degenerate Daehee numbers and polynomials ⋮ Unnamed Item

Cites Work

• Identities involving values of Bernstein, \(q\)-Bernoulli, and \(q\)-Euler polynomials
• \(q\)-Volkenborn integration
• A degenerate Staudt-Clausen theorem
• Symmetry properties of higher-order Bernoulli polynomials
• Symmetryp-adic invariant integral on ℤ_pfor Bernoulli and Euler polynomials
• Higher-order Cauchy of the second kind and poly-Cauchy of the second kind mixed type polynomials
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