Surely this text is designed as a helpful guide to those intending to study Special Functions of mathematical physics with the elementary knowledge of calculus. The starting point of this text is to discuss the solution of second-order differential equation in terms of power series by the usual method of Frobenius. The author does not hesitate to sacrifice brevity for the young readers. The whole of the text would be easily accessible to a reader having little knowledge of complex variable theory.
The subject-matter is divided into ten chapters: (1) Series solutions of differential equations, (2) Gamma and Beta functions, (3) Legendre polynomials and functions, (4) Bessel functions, (5) Hermite polynomials, (6) Laguerre polynomials, (7) Chebyshev polynomials, (8) Gegenbauer and Jacobi polynomials, (9, Hypergeometric functions, (10) Other special functions, such as incomplete gamma functions, error functions and related functions, Riemann’s zeta functions, elliptic integrals, etc.
There is a tabulation of main results in three appendices, viz. differential equations, orthogonality relations and generating functions.
The problems at the end of each chapter are very interesting and some hints and solutions are also provided.