On Various Forms of Solution of k-Hypergeometric Differential Equations

Nafis  Ahmad

doi:10.59828/pijms.v2i4.45

Authors

Nafis Ahmad Department of Mathematics, Shibli National College, Azamgarh, U.P., India Author https://orcid.org/0009-0007-5368-2542

DOI:

https://doi.org/10.59828/pijms.v2i4.45

Keywords:

k-hypergeometric equations; Forbenious method; k-hypergeometric series solutions, regular singular point.

Abstract

In this paper, the series solutions of the second order k-hypergeometric differential equation based on the Frobenious method have been discussed. First, we obtained two linearly independent solutions and then the two derived forms each valid in their respective complex region characterize by the regular singular points of this differential equation. The main objective of the paper is to present the existence of various forms of solutions of the k-hypergeometric differential equation valid in different regions of the complex z-plane.