Generalized Integral Transforms of Incomplete R-Functions

Abstract

Advanced integral transformations utilizing the incomplete $R$-functions, a category about generalized special functions, are examined in this study. We thoroughly prove image formulae of the incomplete $R$-functions using two new integral transforms: the general integral transform and the generalized Bessel-Maitland integral transform. A few existing integral transformations for the range of special functions are assessed using these relations.
Our results lay the groundwork for more research into incomplete $R$-functions and their usefulness in intricate numerical and analytical frameworks.