A CLASS OF I-FUNCTIONS
By
V. P. Saxena
Jiwaji University, Gwalior, Madhya Pradesh, India-474011 & The Mathematics Consortium, Pune, Maharashtra, India-411004
Email: vinodpsaxena@gmail.com
(Received: August 17, 2025; In format: August 20, 2025; Revised: September 10, 2025; Accepted: September 20, 2025)
DOI: https://doi.org/10.58250/jnanabha.2025.55204
Abstract
The I-Function introduced by the author [4] is the ultimate generalization of all the hypergeometric functions series or complex integrals (like E and H-Functions). This function was based on the generalized Hardy-Titchmarsh theorems for symmetric and unsymmetric Fourier kernels. However, there is a class of I-Functions which have not come to the light in spite of their potential applications in science, engineering and artificial intelligence (AI). The purpose of this paper is to introduce such functions. This investigation may be useful in finding solutions of differential and Integral equations arising in mixed boundary value problems of Physics, Engineering and Biology.
2020 Mathematical Sciences Classification: 33C45, 33C60.
Keywords and Phrases: I-Function, Mellin-Barne’s Integrals, Hypergeometric Functions, Bessel Functions.