CERTAIN INTEGRALS INVOLVING MULTIVARIABLE GENERAL CLASS OF POLYNOMIAL, JACOBI POLYNOMIALS AND I-FUNCTION OF TWO VARIABLES
By
Dheerandra Shanker Sachan
St.Mary’s Postgraduate College, Vidisha, Madhya Pradesh, India-464001
Email: sachan.dheerandra17@gmail.com
(Received: June 01, 2025; In format: June 10, 2025; Revised: June 18, 2025; Accepted June 20, 2025)
DOI: https://doi.org/10.58250/jnanabha.2025.55127
Abstract
The aim of this paper is to establish unified integrals that encompass a diverse set of elements, including multivariable general class of polynomials, Jacobi polynomials, and the I-function of two variables. Initially, we computed integrals involving multivariable general class of polynomials and the I-function of two variables using the Oberhettinger formula. Subsequently, we derived integrals involving Jacobi polynomials and the I-function of two variables. Due to the general nature of I-function of two variables, we also derived specific integrals involving the I-function and the H-function of one variable as special cases based on our primary findings.
2020 Mathematical Sciences Classification: 33B15, 33E12, 33C60, 44A20
Keywords and Phrases: Multivariable general class of polynomials, Oberhettinger formula, Jacobi polynomials, Fox’s H-function, I-function of one variables, I-function of two variables.