KAJIAN FUNGSI HIPERGEOMETRIK DAN FUNGSI HIPERGEOMETRIK KONFLUEN SERTA APLIKASINYA DALAM MENENTUKAN SOLUSI PERSAMAAN DIFERENSIAL BIASA (PDB) ORDE DUA

Abstract

Hypergeometric function and Confluent Hypergeometric functions are built by the concept of the Hypergeometric series and Confluent Hypergeometric series.
Hypergeometric function is a solution to the Hypergeometric equation while the Confluent Hypergeometric function is a solution to the Confluenty pergeometric equation. Hypergeometric equation and Confluent Hypergeometric equation are the equations in the form of a second order differential equation. The purpose of this research is to find the solutions of second order ordinary differential equations using the approaches Hypergeometric series and Confluent Hypergeometric series by observing regular singular point of the ordinary differential equations. In this research indicates that the second order ordinary differential equation xyⁿ + (1+x) y' - { (m² / x) + y } y=0 has a regular singular point. Therefore, this differential equation has series solution that can be written as Confluent Hypergeometric function.