Study of Recent Advances in Special Functions and Their Computer Algebra

Abstract

Investigation into Special Functions using computer algebra has recently become a rising newlinearea in the field of research. The study of recent advances in Special Functions and their newlinecomputer algebra describe the latest advances in Special Functions and their computer newlinealgebra. The subject matter presented in this thesis has been separated into VIII chapters. newlineThe I chapter introduces a brief introduction of Special Functions, the aim of our research, and a summary of all the chapters. The II chapter is devoted to our study and a survey of the inputs made by earlier researchers on the topic covered in the thesis, as well as an explanation of the inquiry and review of the material found to complete the research effort. In the III chapter, a multivariate generalized Mittag-Leffler function is investigated by two generalized integral formulas in this chapter, which are explained in the form of newlinethe Lauricella series. We also presented the computer algebra for certain unified integrals including the generalized Mittag-Leffler function. In the IV chapter, The examination of a few unified integrals produced for generalized Mittag-Leffler function is the focus of this chapter. We included computer algebra for unified integrals for the generalized Mittag- newlineLeffler functions. We created the generalized fractional integral formulas in chapter V. newlineWe employed the integral operators provided by Saigo in the form of the interaction newlinebetween the H-function and the generalized Mittag-Leffler function to obtain the desired newlineresults. In the VI chapter, we discuss generalized fractional integrals, which involved the production of two H-functions and generalized Mittag-Leffler function.