On the modified q-Genocchi numbers and polynomials and their\n applications

2013/11/23 by Serkan Araci, Serkan Aracı, Armen Bagdasaryan +8
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebra over a field #Analytic Number Theory Research #Combinatorics #Difference polynomials #Discrete mathematics #Discrete orthogonal polynomials #FOS: Mathematics #Generating function #Koornwinder polynomials #Macdonald polynomials #Mathematical Inequalities and Applications #Mathematical functions and polynomials #Mathematics #Multiplication (music) #Number Theory (math.NT) #Orthogonal polynomials #Pure mathematics #Transformation (genetics) #math.NT

paper · pdf · doi:10.48550/arxiv.1311.5992

10 pages; submitted

arxiv created 2013/11/23 · openalex publication_date 2013/11/23 · arxiv updated 2013/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The main objective of this paper is to introduce the modified q-Genocchi\npolynomials and to define their generating function. In the paper, we show new\nrelations, which are explicit formula, derivative formula, multiplication\nformula, and some others, for mentioned q-Genocchi polynomials. By applying\nMellin transformation to the generating function of the modified q-Genocchi\npolynomials, we define q-Genocchi zeta-type functions which are interpolated by\nthe modified q-Genocchi polynomials at negative integers.\n

Citations

• Generating functions for q-Bernstein, q-Meyer-Konig-Zeller and q-Beta basis
• Some identities and an explicit formula for Bernoulli and Stirling numbers

Related

• A note on the q-Genocchi numbers and polynomials
• A family of generalized q-Genocchi numbers and polynomials
• A new class of generalized Genocchi polynomials
• New approach to q-Genocch, Euler numbers and polynomials and their interpolation functions
• q-Fibonacci polynomials and q-Genocchi numbers