On some linear combination of two contiguous hypergeometric functions

TL;DR

This paper investigates the asymptotic behavior of specific linear combinations of two contiguous hypergeometric functions using contiguous relations, under certain parameter conditions.

Contribution

It provides new asymptotic analysis for linear combinations of hypergeometric functions based on contiguous relations, expanding understanding of their behavior.

Findings

Derived asymptotic formulas for hypergeometric combinations

Identified conditions affecting asymptotic behavior

Enhanced analytical tools for hypergeometric functions

Abstract

The aim of this paper is to give, using some contiguous relations, the asymptotic behaviour of some linear combination of two symmetric contiguous hypergeometric functions, under some conditions of their parameters.