Developments of the I-Function Several Complex Variables

The purpose of this study is to present the I-function of r-variables, a natural extension of thepopular, intriguing, and practical Fox H-function. The results are quite generalized when r=1, at which pointwe get the I-function. Second, we showed that an integral is formed by multiplying the I-function of a singlevariable by the Bessel function and the General polynomial class. A two-variable I-function may be obtainedby evaluating the Sine transform of the product of the Hermite polynomial and Fox's H-function, and itsspecial case, the Cosine transform of the product of the Legendre polynomial and Fox's H-function. Wehave also provided exceptional examples, basic features, and circumstances under which convergenceoccurs. Results for H-functions in r variables are generalized in this study.