Relationships between Mahler Expansion and Higher Order q-Daehee Polynomials

Abstract

In this paper, we derive multifarious relationships among the two types of higher order q-Daehee polynomials and p-adic gamma function via Mahler theorem. Also, we compute some weighted p-adic q-integrals of the derivative of p-adic gamma function related to the Stirling numbers of the both kinds and the q-Bernoulli polynomials of order k.

Keywords

• q-numbers
• p-adic numbers
• p-adic gamma function
• Mahler expansion
• Bernoulli polynomials
• Daehee polynomials
• Stirling numbers of the first kind
• Stirling numbers of the second kind

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