TWO-DIMENSIONAL INTEGRAL TRANSFORMATIONS WITH KUMMER FUNCTION
 AND HYPERGEOMETRIC GAUSSIAN FUNCTION IN KERNELS AS SPECIAL CASES
 OF TWO-DIMENSIONAL INTEGRAL G-TRANSFORMATION

Abstract

Two two-dimensional integral transformations with confluent hypergeometric Kummer function and Gauss hypergeometric function in kernels are considered. Applying the Mellin transformation technique, we show that they are special cases of a two-dimensional G-transformation. Based on the theory of the G-transformation, the properties of the considered integral transformations in the weight spaces of integrable functions in the domain  are investigated. The results of the study generalize the results obtained earlier for the corresponding one-dimensional analogues.