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2023•International Journal of Scientific Research in Modern Science and TechnologyOpen access

On Extended Transformation Formulae Associated to the k-Hypergeometric Function

Nafis Ahmad

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Abstract

Recently the second order homogeneous k-hypergeometric differential equation and the definition of the function as its solution at the origin have been presented. Motivated by the current research work in the study of k-hypergeometric functions, our aim is to establish certain extended transformation formulae related to the k-hypergeometric function with the Euler's identity for Gauss hypergeometric function as a special case.

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What this paper is about

Recently the second order homogeneous k-hypergeometric differential equation and the definition of the function as its solution at the origin have been presented. Motivated by the current research work in the study of k-hypergeometric functions, our aim is to establish certain extended transformation formulae related to the k-hypergeometric function with the Euler's identity for Gauss hypergeometric function as a special case.

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Available abstract

Recently the second order homogeneous k-hypergeometric differential equation and the definition of the function as its solution at the origin have been presented. Motivated by the current research work in the study of k-hypergeometric functions, our aim is to establish certain extended transformation formulae related to the k-hypergeometric function with the Euler's identity for Gauss hypergeometric function as a special case.

Key concepts: Basic hypergeometric series, Confluent hypergeometric function, Generalized hypergeometric function, Hypergeometric function of a matrix argument, Hypergeometric identity, Bilateral hypergeometric series, Frobenius solution to the hypergeometric equation, Hypergeometric function

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