# Volume 8 Issue 2 ( June 2021 )

Pages_290-295

## Solutions of Hypergeometric ODE with b Equal to c for Any x

### Djarot B. Darmadi, Lilis Yuliati, Marco Talice

#### [ABSTRACT]

The hypergeometric Ordinary Differential Equation (ODE) has wide application in the Mechanical Engineering field. The solution to the hypergeometric ODE is called a hypergeometric function, or also a hypergeometric series. Not all of the hypergeometric series converges to a simple defined algebraic function. It is a well-known fact that the hypergeometric series F(1, *c*, *c*; x) will converge to the Maclaurin series 1/(1-x). This article investigates the hypergeometric function F(k, *c*, *c*; x). It will be proven that the function F(*k*, *c*, *c*; x) will always converge to certain values. We can represent these values on a line of the form *A* + mx, whose coefficients *A* and m are functions of x.

**Keywords: hypergeometric ODE; hypergeometric function; hypergeometric series.**