Open AccessInvestigation of Extended k-Hypergeometric Functions and Associated Fractional Integrals
Author(s) -
Mohamed Abdalla,
Muajebah Hidan,
Salah Boulaaras,
Bahri Cherif
Publication year - 2021
Publication title -
mathematical problems in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.262
H-Index - 62
eISSN - 1026-7077
pISSN - 1024-123X
DOI - 10.1155/2021/9924265
Subject(s) - hypergeometric function , mathematics , special functions , hypergeometric identity , hypergeometric function of a matrix argument , generalized hypergeometric function , gauss , basic hypergeometric series , barnes integral , confluent hypergeometric function , appell series , hypergeometric distribution , bilateral hypergeometric series , pure mathematics , convergence (economics) , fractional calculus , mathematical analysis , physics , quantum mechanics , economics , economic growth
Hypergeometric functions have many applications in various areas of mathematical analysis, probability theory, physics, and engineering. Very recently, Hidan et al. (Math. Probl. Eng., ID 5535962, 2021) introduced the (p, k)-extended hypergeometric functions and their various applications. In this line of research, we present an expansion of the k-Gauss hypergeometric functions and investigate its several properties, including, its convergence properties, derivative formulas, integral representations, contiguous function relations, differential equations, and fractional integral operators. Furthermore, the current results contain several of the familiar special functions as particular cases, and this extension may enrich the theory of special functions.