New Addition Formulae Using Hypergeometric Functions Via Gamma Function Representations | Chapter 4 | Mathematics and Computer Science: Research Updates Vol. 6

 

The discovery of a hypergeometric function has provided an intrinsic stimulation in the world of mathematics. It has also motivated the development of several domains such as complex functions, Riemann surfaces, differential equations, difference equations, arithmetic theory and so forth. The global structure of the Gauss hypergeometric function as a complex function, i.e., the properties of its monodromy and the analytic continuation, has been extensively studied by Riemann. His method is based on complex integrals. Moreover, when the parameters are rational numbers, its relation to the period integral of algebraicm curves became clear, and a fascinating problem on the uniformization of a Riemann surface was proposed by Riemann and Schwarz. On the other hand, Kummer has contributed a lot to the research of arithmetic properties of hypergeometric functions. But there, the main object was the Gauss hypergeometric function of one variable. The solution of many problems In this chapter we have developed certain addition formulae using Hypergeometric function in the form of Gamma function. The formulae which are developed here are all new.

 

Author(s) Details

 Salah Uddin
Department of Mathematics, AMET University, Kanathur, Chennai, Tamilnadu, India.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcsru/v6/5678