AN INCOMPLETE CATEGORY COMPRISED OF R-FUNCTIONS AND THEIR APPLICATIONS

Our investigation is based upon a unique and innovative generalization of a contour-type Mellin-Barnes integral representing the R-function, presented by Rathie (1989) for exploring further problems connected with evaluating statistical hypotheses. The goal regarding this attempt is to investigate another group of special functions associated with the R-function, propose an incomplete extension of the R-function, and highlight unique features of these functions due to the existence of gamma functions of incomplete type. We investigate and evaluate certain remarkable aspects of these incomplete R-functions, such as formulae for derivative, decomposition, reduction, integral representations, and fractional calculus among other things. In addition, the primary findings have been utilized to illustrate potentially novel findings, containing the R-function in the particular instance.