Some transformations and integral representations of horn's functions

• V. Kim Tuan Bielorrusia State University
• S. L. Kalla Universidad del Zulia-Venezuela

Resumo

 

Horn gave the general definition of hypergeometric functions of two variables. There are thirty four hypergeometric functions of two variables of this type. Fourteen functions are complete and the remaining twenty are the confluente cases. This includes the four Appell functions and seven Humbert functions. In this work we obtain number of transformation formulae end integral representation; for Horn functions, The transformation formuIae for Gauss' hypergeometric function and Kummer function are used to obtain some new results. The results established here give some new formulae for analytic continuation of Horn function in various domains and to study their behaviour in the neighbourhood of singular points.