Abstract
The main purpose of this paper is to introduce and investigate a new class of generalized q-Bernoulli and q-Euler polynomials. The q-analogues of well-known formulas are derived. A generalization of the Srivastava-Pintér addition theorem is obtained.
Highlights
1 Introduction Throughout this paper, we always make use of the following notation: N denotes the set of natural numbers, N denotes the set of nonnegative integers, R denotes the set of real numbers, C denotes the set of complex numbers
The q-polynomial coefficient is defined by n =
Motivated by the generalizations in ( ) of the classical Bernoulli and Euler polynomials, we introduce and investigate here the so-called generalized two-dimensional q-Bernoulli and q-Euler polynomials, which are defined as follows
Summary
Natalini and Bernardini [ ], Bretti et al [ ], Kurt [ , ], Tremblay et al [ , ] studied the properties of the following generalized Bernoulli and Euler polynomials: tm et – Motivated by the generalizations in ( ) of the classical Bernoulli and Euler polynomials, we introduce and investigate here the so-called generalized two-dimensional q-Bernoulli and q-Euler polynomials, which are defined as follows. The generalized two-dimensional qBernoulli polynomials Bn[m,q– ,α](x, y) are defined, in a suitable neighborhood of t = , by means of the generating function tm eq(t) – Tm– ,q(t) The generalized two-dimensional q-Euler polynomials En[m,q– ,α](x, y) are defined, in a suitable neighborhood of t = , by means of the generating functions
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