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An Identity for Generalized Euler Polynomials

Chellal Redha

Abstract

In this paper, we introduce a novel identity for generalized Euler polynomials, leading to further generalizations for several relations involving classical Euler numbers, Euler polynomials, Genocchi polynomials, and Genocchi numbers.

An Identity for Generalized Euler Polynomials

Abstract

In this paper, we introduce a novel identity for generalized Euler polynomials, leading to further generalizations for several relations involving classical Euler numbers, Euler polynomials, Genocchi polynomials, and Genocchi numbers.
Paper Structure (5 sections, 10 theorems, 36 equations)

This paper contains 5 sections, 10 theorems, 36 equations.

Table of Contents

  1. Introduction
  2. Some properties of the generalized Euler polynomials and lemmas
  3. Main result
  4. Applications
  5. Conclusion

Key Result

Lemma 1

For every non-negative $n$ and for all complex numbers $\alpha$ and $\gamma$, one has

Theorems & Definitions (14)

  • Lemma 1
  • Lemma 2
  • proof : Proof of Eq. (\ref{['r7']})
  • proof : Proof of Eq. (\ref{['r8']})
  • Theorem 3
  • proof
  • Corollary 4
  • Corollary 5
  • proof
  • Corollary 6
  • ...and 4 more