ABSTRACT
Special functions of a complex variable are a vast subject exhaustively studied by the mathematicians of the last century. In the very brief treatment can only study a few of the most important points. A comprehensive treatment is given by Whittaker and Watson and briefer treatments by Copson and Carrier, M. Krook and C. E. Pearson. This function F(a,b;c;z) is a very general one and depends on three complex parameters a,b,c as well as the complex variable z. The confluent hypergeometric function is important in applications. The solutions of the quantum mechanical coulomb scattering problem are expressed in terms of it; this application is discussed in some detail in the book by N. F. Mott and H. S. W. Massey.
