Generalize Hypergeometric Series And Some Its Application

This paper mainly introduces the basic contents of hypergeometric series.Secondly,the hypergeometric series is generalized to obtain generalized hypergeometric series,and some properties and applications of generalized hypergeometric series are given.The main contents of the paper are as follows:1.The hypergeometric series is generalized to obtain generalized hypergeometric series.We use the Legendre inversion formula to prove three generalized hypergeometric series identities.Furthermore,the linear combination between generalized hypergeometric series is used to obtain a new generalized super Geometric progression identities.2.Taking the hypergeometric equation as the starting point,the hypergeometric equation is generalized to obtain the generalized hypergeometric equation,and the solution of the generalized hypergeometric equation is expressed by the generalized hypergeometric series.Finally,the concept of the adjacent function of the generalized hypergeometric series is given.The relationship between several generalized hypergeometric series neighbor functions is proved.