Mathematical Methods in the Applied Sciences

Research Article

Srivastava–Pintér theorems for 2D-Appell polynomials and their applications

Corresponding Author

M. Ali Özarslan

Department of Mathematics, Eastern Mediterranean University, Gazimagusa, TRNC, Mersin 10, Turkey

Correspondence to: M. Ali Özarslan, Department of Mathematics, Eastern Mediterranean University, Gazimagusa, TRNC, Mersin 10, Turkey.

E-mail: [email protected]

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S. Gaboury,

S. Gaboury

Department of Mathematics and Computer Science, University of Quebec at Chicoutimi, QC, Canada, G7H 2B1

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M. Ali Özarslan,

Corresponding Author

M. Ali Özarslan

Department of Mathematics, Eastern Mediterranean University, Gazimagusa, TRNC, Mersin 10, Turkey

Correspondence to: M. Ali Özarslan, Department of Mathematics, Eastern Mediterranean University, Gazimagusa, TRNC, Mersin 10, Turkey.

E-mail: [email protected]

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S. Gaboury,

S. Gaboury

Department of Mathematics and Computer Science, University of Quebec at Chicoutimi, QC, Canada, G7H 2B1

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First published: 13 September 2013

https://doi.org/10.1002/mma.2965

Citations: 3

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Abstract

Recently, Srivastava and Pintér proved addition theorems for the generalized Bernoulli and Euler polynomials. Luo and Srivastava obtained the anologous results for the generalized Apostol–Bernoulli polynomials and the generalized Apostol–Euler polynomials. Finally, Tremblay et al. gave analogues of the Srivastava–Pintér addition theorem for general family of Bernoulli polynomials. In this paper, we obtain Srivastava–Pintér type theorems for 2D-Appell Polynomials. We also give the representation of 2D-Appell Polynomials in terms of the Stirling numbers of the second kind and 1D-Appell polynomials. Furthermore, we introduce the unified 2D-Apostol polynomials. In particular, we obtain some relations between that family of polynomials and the generalized Hurwitz–Lerch zeta function as well as the Gauss hypergeometric function. Finally, we present some applications of Srivastava–Pintér type theorems for 2D-Appell Polynomials. Copyright © 2013 John Wiley & Sons, Ltd.

References

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Volume37, Issue15

October 2014

Pages 2198-2210

Srivastava–Pintér theorems for 2D-Appell polynomials and their applications

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Srivastava–Pintér theorems for 2D-Appell polynomials and their applications

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