# ON p-ADIC INTEGRAL FOR GENERALIZED DEGENERATE HERMITE-BERNOULLI POLYNOMIALS ATTACHED TO χ OF HIGHER ORDER

• Accepted : 2019.01.14
• Published : 2019.03.25
• 17 0

#### Abstract

In the current investigation, we obtain the generating function for Hermite-based degenerate Bernoulli polynomials attached to ${\chi}$ of higher order using p-adic methods over the ring of integers. Useful identities, formulae and relations with well known families of polynomials and numbers including the Bernoulli numbers, Daehee numbers and the Stirling numbers are established. We also give identities of symmetry and additive property for Hermite-based generalized degenerate Bernoulli polynomials attached to ${\chi}$ of higher order. Results are supported by remarks and corollaries.

#### Keywords

Multivariate p-adic integral;Generalized degenerate Bernoulli polynomials;Hermite polynomials;Daehee numbers;Stirling numbers