Abstract
The aim of this paper is to investigate and give a new family of multi-variable Apostol-type polynomials. This family is related to Apostol-Euler, Apostol-Bernoulli, Apostol-Genocchi and Apostol-laguerre polynomials. Moreover, we derive some implicit summation formulae and general symmetry identities. The new family of polynomials introduced here, gives many interesting special cases.
Highlights
The 2-variable general polynomials (2VGP) pn(x, y) are defined by, [10] (1) ext φ(y, t) = ∞tn pn(x, y) n!, p0(x, y) = 1, n=0 where φ(y, t) has series expansion tn (2)φ(y, t) = φn(y) n!, φ0(y) = 0. n=0These polynomials pn(x, y) have many intersting special polynomials of two variables
El-Desouky and Gomaa [5] introduced a unification of multiparameter Apostol-type polynomials by means of the following generating function
=j between the multi-Variable Unified Family of Generalized Apostol-Euler, Bernoulli and Genocchi polynomials and Stirling number of second kind
Summary
El-Desouky and Gomaa [5] introduced a unification of multiparameter Apostol-type polynomials by means of the following generating function The multi-variable unified family of generalized Apostol-Euler, Bernoulli and Genocchi polynomials are introduced and investigate their properties. 2. THE MULTI-VARIABLE UNIFIED FAMILY OF GENERALIZED APOSTOL-EULER, BERNOULLI AND GENOCCHI POLYNOMIALS
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