Mellin convolutions of products and ratios

Abstract

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Usually, convolution refers to Laplace convolution in the literature, but Mellin convolutions can yield very ueful results. This aspect is illustrated in the coming sections. This study deals with Mellin convolutions of products and ratios. Functions belonging to the pathway family of functions are considered. Several types of integral representations, their equivalent representations in terms of G and H-functions, and their equivalent computable series representations are examined in this study.Mathematics Subject Classification 2010: 26A33, 44A10, 33C60, 35J10.

Keywords

• special functions
• Mellin convolutions
• H-function
• G-function
• integral transform
• Laplace transform