On the analogs of Euler numbers and polynomials associated with p-adic q-integral on Zp at q=−1

By Taekyun Kim. 2007

134 citations recorded by the source corpus.

Abstract The purpose of this paper is to construct λ-Euler numbers and polynomials by using fermionic expression of p-adic q-integral at q = − 1 . From these λ-Euler polynomials, we derive the harmonic sums of higher order. Finally, we investigate several interesting properties and relationships involving the classical as well as the generalized Euler numbers and polynomials. As an application, we will treat p-adic invariant integrals on Z p involving trigonometric functions.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/712025c41978bd2cab1929882cb0d8167982e344

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In Algebra and Number Theory

1. Yilmaz Simsek
2. Taekyun Kim
3. Veli Kurt
4. Hari M. Srivastava
5. Daeyeoul Kim

In Discrete Mathematics and Combinatorics

1. Yilmaz Simsek
2. Taekyun Kim

Citations in the corpus

• Explicit formulas for p-adic integrals: approach to p-adic distributions and some families of special numbers and polynomials. (2019, background): “172], [57]); ∫”
• Construction of some new families of Apostol-type numbers and polynomials via Dirichlet character and p-adic q-integrals (2018, unknown): “[19, 21, 39] and the references cited therein).”
• Complete sum of products of (h, q)-extension of Euler polynomials and numbers (2010, methodology): “In [7], [8], [ 10 ], Kim construced p-adic q-Volkenborn integral identities.”