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We solve the second-order linear differential equation called the k-hypergeometric differential equation by using Frobenius method around all its regular singularities. At each singularity, we find 8 solutions corresponding to the different cases for parameters and modified our solutions accordingly. [ABSTRACT FROM AUTHOR]

The main objective of the present paper is to define k-gamma and k-beta distributions and moments generating function for the said distributions in terms of a new parameter k > 0. Also, the authors prove some properties of these newly defined distributions. [ABSTRACT FROM AUTHOR]

In this research work, our aim is to determine the contiguous function relations for fc-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 → 1, then the contiguous function relations for fc-hypergeometric functions are Gauss contiguous function relations. [ABSTRACT FROM AUTHOR]

In this research work, our aimis to determine the contiguous function relations for κ-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 κ > 0. Obviously if κ → 1, then the contiguous function relations for κ-hypergeometric functions are Gauss contiguous function relations. [ABSTRACT FROM AUTHOR]