A Kummer-type transformation for some k-hypergeometric functions

Abstract

In this paper, by applying the differential equation techniques and using integral representations, we obtain the Kummer-type transformations of k-hypergeometric functions ${}_1{F}_{1,k}((a,k);(b,k);x)$ and ${}_2{F}_{2,k}((a,k),(d,k);(b,k),(c,k);x),$ which include known results as special cases.

Keywords:

• Kummer-type transformation
• hypergeometric functions
• k-hypergeometric functions

2020 Mathematics Subject Classifications:

• 33C20
• 33C15

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The present investigation was supported in part by the National Natural Science Foundation of the People's Republic of China [grant number 11201070], and the Science Research Fund of Department of Guangdong Province of the People's Republic of China [grant number Yq2013161].