Identities of Symmetry for Euler Polynomials Arising from Quotients of Fermionic Integrals Invariant under S3

Higher Order Degenerate Hermite-Bernoulli Polynomials Arising from $p$-Adic Integrals on $mathbb{Z}_p$

Our principal interest in this paper is to study higher order degenerate Hermite-Bernoulli polynomials arising from multivariate $p$-adic invariant integrals on $mathbb{Z}_p$. We give interesting identities and properties of these polynomials that are derived using the generating functions and $p$-adic integral equations. Several familiar and new results are shown to follow as special cases. So...

Identities of Symmetry for Carlitz q-Bernoulli Polynomials Arising from q-Volkenborn Integrals on Zp under Symmetry Group S3

AN IDENTITY OF THE SYMMETRY FOR THE FROBENIUS-EULER POLYNOMIALS ASSOCIATED WITH THE FERMIONIC p-ADIC INVARIANT q-INTEGRALS ON Zp

Abstract. The main purpose of this paper is to prove an identity of symmetry for the Frobenius-Euler polynomials. It turns out that the recurrence relation and multiplication theorem for the Frobenius-Euler polynomials which discussed in [ K. Shiratani, S. Yamamoto, On a p-adic interpolation function for the Euler numbers and its derivatives, Memo. Fac. Sci. Kyushu University Ser.A, 39(1985), 1...

Identities of Symmetry for Generalized Higher - Order q - Euler Polynomials under S 3 Dmitry

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, we study the identities of symmetry for the generalized higher-order q-Euler polynomials in three variable under symmetry group S 3 which are derived from the...

Some identities of symmetry for the degenerate q-Bernoulli polynomials under symmetry group of degree n

Recently, Kim-Kim Introduced some interesting identities of symmetry for qBernoulli polynomials under symmetry group of degree n. In this paper, we study the degenerate q-Euler polynomials and derive some identities of symmetry for these polynomials arising from the p-adic q-integral on Zp. AMS subject classification: 11B68, 11S80, 05A19, 05A30.