doi: 10.17706/ijapm.2019.9.3.119-126
Generating Functions for k-Hypergeometric Functions
Duriye Korkmaz-Duzgun
1
,
- 1 Kafkas University, Faculty of Economics and Administrative Sciences, Department of Business Administration, Central Campus TR-36100 Kars, Turkey
- 2 Gazi University, Faculty of Science, Department of Mathematics, 06500 Teknikokullar, Ankara, Turkey.
Abstract
In mathematics, generating functions are important way to transform formal power series into functions and to analyze asymptotic properties of sequences. On the other hand, hypergeometric function is a special function represented by the hypergeometric series. Gauss, Confluent, Appell, Lauricella, and Horn functions are as an example of hypergeometric functions. In this article, we will introduce k-hypergeometric functions which are extensions of the Gauss hypergeometric functions including k- Pochhammer symbol. We first give an identity for k-Pochhammer symbol and certain linear generating functions for k-hypergeometric functions. Then we derive a family of multilinear and multilateral generating functions for these functions. In the main theorems, specially, bilateral generating function relations are obtained by applying extended multivariable hypergeometric functions and Cesáro Polynomials. Additionally we present bilinear generating functions for k-hypergeometric functions.
Keywords
- Hypergeometric functions
- generating functions
- multilinear and multilateral generating functions
- k-hypergeometric functions
- k-Pochhammer symbol
How to Cite
Duriye Korkmaz-Duzgun and Esra Erkus-Duman, "Generating Functions for k-Hypergeometric Functions," International Journal of Applied Physics and Mathematics, vol. 9, no. 3, pp. 119-126, 2019. https://doi.org/ 10.17706/ijapm.2019.9.3.119-126
Copyright & License
Copyright © 2019 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).