Extension of Connecting Formulas on Hypergeometric Function

Abstract

The Hypergeometric series is the extension of the geometric series and the Confluent Hypergeometric Function is the solution of the Hypergeometric Differential Equation. Kummer has developed six solutions for the differential equation and twenty connecting formulas. The connecting formula consist of a solution expressed as the combination of two other solutions. Further extension was done by Poudel et al. This research work has extended the nine connecting formulas obtained by Poudel et al. to obtain the other nine solutions