Abstract
Recently, some identities of degenerate Euler polynomials arising from p-adic fermionic integrals on $\mathbb{Z}_{p}$ were introduced in Kim and Kim (Integral Transforms Spec. Funct. 26(4):295-302, 2015). In this paper, we study degenerate q-Euler polynomials which are derived from p-adic q-integrals on $\mathbb{Z}_{p}$ .
Highlights
Let p be a fixed odd prime number
Throughout this paper, Zp, Qp and Cp will denote the ring of p-adic integers, the field of p-adic rational numbers and the completion of algebraic closure of Qp, respectively
We study q-extensions of the degenerate Euler polynomials and give some formulae and identities of those polynomials which are derived from the fermionic p-adic q-integrals on Zp
Summary
Let p be a fixed odd prime number. Throughout this paper, Zp, Qp and Cp will denote the ring of p-adic integers, the field of p-adic rational numbers and the completion of algebraic closure of Qp, respectively. ), we get qI–q(f ) + I–q(f ) = [ ]qf ( ) f (x) = f (x + ) , The degenerate Euler polynomials of order r (∈ N) are defined by the generating function to be En(r)(x) where En(r)(x) are the higher-order Euler polynomials.
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