Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials*

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Abstract

Recently, Srivastava and Pintér [1] investigated several interesting properties and relationships involving the classical as well as the generalized (or higher-order) Bernoulli and Euler polynomials. They also showed (among other things) that the main relationship (proven earlier by Cheon [2]) can easily be put in a much more general setting. The main object of the present sequel to these earlier works is to derive several general properties and relationships involving the Apostol-Bernoulli and Apostol-Euler polynomials. Some of these general results can indeed be suitably specialized in order to deduce the corresponding properties and relationships involving the (generalized) Bernoulli and (generalized) Euler polynomials. Other relationships associated with the Stirling numbers of the second kind are also considered.

Keywords

ernoulli polynomials and numbers
Euler polynomials and numbers
Generalized (or higher-order) Bernoulli polynomials and numbers
Generalized (or higher-order) Euler polynomials and numbers, Apostol-Bernoulli polynomials and numbers, Apostol-Euler polynomials and numbers, Generalized Apostol-Bernoulli polynomials and numbers, Generalized Apostol-Euler polynomials and numbers, Stirling numbers of the second kind, Generating functions, Srivastava-Pintér addition theorems, Recursion formulas

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*

The present investigation was supported, in part, by the National Natural Science Foundation of the People's Republic of China under Grant 10001016 and the Natural Sciences and Engineering Research Council of Canada under Grant OGP0007353.