Title: A Study of Unified Integrals Involving the Generalized Legendre's Associated Function, the generalized Polynomial Set and H-Function with Applications


Shalini Shekhawat

Department of Mathematics, Swami Keshvanand Institute of Technology, Management & Gramothan Jaipur-302017, (INDIA),

Sanjay Bhattar

Department of Mathematics, Malaviya National Institute of Technology, Jaipur-302017 (INDIA)

Pages: 62-70


The aim of this paper is to evaluate three finite integrals  involving the product of generalized Legendre associated function, generalized polynomial set and H -function proposed by Inayat Hussain (1987) [6] which contain a certain class of Feynman integrals. Next, we establish three theorems as an application of our main findings and using three results of Orr and Bailey recorded in the well-known text by Slater [11]. Further, we evaluate certain new integrals by the applications of these Theorems, which are of interest themselves and sufficiently general in nature. Several new and known results follow as their special cases. For the sake of illustration, some special cases are mentioned briefly.

Hypergeometric Function, H -function, Legendre polynomial, Generalized polynomial set