Connection Formulas on Kummer’s Solutions and their Extension on Hypergeometric Function

Abstract

Abstract: Hypergeometric functions are transcendental functions that are applicable in various branches of mathematics, physics, and engineering. They are solutions to a class of differential equations called hypergeometric differential equations. Kummer obtained six solutions for the hypergeometric differential equation and twenty connection formulae. This research work has extended those connection formulas to other six solutions   y1(x),y2(x), y3(x), y4(x), y5(x) and y6(x) show that each solution can be expressed in terms of linear relationship among three of the other solutions. 

Keywords: Hypergeometric function, Kummer’s formula, Connection formula