On a Class of Macrobert’s Type Finite Integrals Involving Generalized Hypergeometric Functions

Abstract

The classical hypergeometric summation theorems have a significant role in the theory of generalized hypergeometric functions. Over the years generalization and extension of classical summation theorems for the series $${_{q+1}}F_q$$ , and their applications have been the predominant area of research. Notably, Masjed-Jamei and Koepf (2018) extended these classical summation theorems for the series $${_{q+1}}F_q$$ for $$q=1,2,3,4,5 $$ , and explored a variety of provocative instances of their key discoveries. These findings were recently applied by Jun et al. (2019) in the evaluation of single integrals, double integrals, and Laplace-type integrals. The main aim of this paper is to elucidate eleven Eulerian’s integrals of MacRobert’s type involving generalized hypergeometric functions. This is accomplished by combining an intriguing integral given by MacRobert with the extended summation theorems due to Masjed-Jamei and Koepf (2018). Additionally, there are a few interesting specific illustrations of our main findings which are based on prior findings derived by Jun et al. (2019). The results are clear, appealing, and logical along with the potential for further applications.