Certain Laplace transforms of convolution type integrals involving product of two special pFp functions

Abstract

Recently the authors obtained several Laplace transforms of convolution type integrals involving Kummer’s function 1F1 [Appl. Anal. Discrete Math., 2018, 12(1), 257-272]. In this paper, the authors aim at presenting several new and interesting Laplace transforms of convolution type integrals involving product of two special generalized hypergeometric functions pFp by employing classical summation theorems for the series 2F1, 3F2, 4F3 and 5F4 available in the literature.

Keywords

• Gauss’s summation theorem
• Gauss’s second summation theorem
• Bailey’s summation theorem
• Kummer’s summation theorem
• Watson’s summation theorem
• Dixon’s summation theorem
• Whipple’s first and second summation theorems
• Dougall’s theorem
• Laplace transform
• Convolution type integrals
• Primary 33C20
• Secondary 33C05
• 33C90