This book is applicable for the study in mathematics using Applications of some Hypergeometric function for UG level and PG level of all Indian universities. Book contain Some Fractional Derivatives Formulae, Double Integral formulae of - Function, Some Integral Formulae and Fourier series of -Function also Application of Hypergeometric Function in Biological Populations and Physical problems.'Hypergeometric' was first used by Wallis in oxford as early as 1655 in his work Arithmetrica Infinitorum when referring to any series which could be regarded as feneralization of the ordinary geometric series.