Abstract—Recently, there are many interested studies including various families of multiple hypergeometric functions and extended hypergeometric functions. Here, we will study on extended multivariable fourth type Horn functions which are both extended and multiple hypergeometric functions. In this article, we establish some generating functions for the extended multivariable fourth type Horn functions and then obtain a family of multilinear and multilateral generating functions for each of them. We also give special cases of the results presented in this paper.

Index Terms—Multiple hypergeometric functions, extended multivariable fourth type Horn functions, horn functions, generating functions, multilinear and multilateral generating functions.

The authors are with Kafkas University, Faculty of Economics and Administrative Sciences, Department of Business Administration, Central Campus TR-36100, Kars, Turkey. They are also with Gazi University, Faculty of Science, Department of Mathematics, TR-06500 Teknikokullar, Ankara, Turkey (email: dkduzgun@kafkas.edu.tr; dryekorkmaz@gmail.com).

Cite: Duriye Korkmaz-Duzgun, Esra Erkuş-Duman, "Generating Functions for the Extended Multivariable Fourth Type Horn Functions," International Journal of Applied Physics and Mathematics vol. 10, no. 2, pp. 65-72, 2020.

Copyright © 2020 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).