Contiguous function relations for \(k\)-hypergeometric functions (Q2016490)

Summary: In this research work, our aim is to determine the contiguous function relations for \(k\)-hypergeometric functions with one parameter corresponding to Gauss fifteen contiguous function relations for hypergeometric functions and also obtain contiguous function relations for two parameters. Throughout in this research paper, we find out the contiguous function relations for both the cases in terms of a new parameter \(k>0\). Obviously if \(k\to 1\), then the contiguous function relations for \(k\)-hypergeometric functions are Gauss contiguous function relations.