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This book has been designed to meet the requirements of the candidates appearing in M.Sc., M.Phil. and Research of various Universities.this book is an outcome of the experience of authors in teaching and research on Generalized hypergeometric function.In this book discus about relation between Double Laplace transform and Double Mellin transform and Double Hankel transform in terms of generalized hypergeometric function with application.A unified study of Astrophysical Thermonuclear function for Boltzmaan-Gibbs statistics and Tsallis statistics or some unified theorems involving the Laplace transform, Convolution integral equation with kernel as a generalized hypergeometric function and H- function of two variables. I am thankful to LAMBERT Academic publishing, Germany for showing faith in me and bringing out this book so nicely.