Generating Functions for q-Apostol Type Frobenius–Euler Numbers and Polynomials

Axioms

关键词: Euler Numbers;    Frobenius–Euler Numbers;    Frobenius–Euler polynomials;    q-Frobenius–Euler polynomials;    q-series;    Generating function;   

DOI  :  10.3390/axioms1030395

来源: mdpi

【 摘 要 】

The aim of this paper is to construct generating functions, related to nonnegative real parameters, for q-Eulerian type polynomials and numbers (or q-Apostol type Frobenius–Euler polynomials and numbers). We derive some identities for these polynomials and numbers based on the generating functions and functional equations. We also give multiplication formula for the generalized Apostol type Frobenius–Euler polynomials.

【 授权许可】

CC BY   
© 2012 by the authors; licensee MDPI, Basel, Switzerland.