Nikiforov A.F., Uvarov V.B. Special functions of mathematical physics: A unified introduction with applications

Boston: Birkhäusеr, 1988. — 427 p.Authors of this book have collected the material on special functions that is most important in mathematical physics and quantum mechanics. They have not attempted to provide the most extensive collection possible of information about special functions, but have set ourselves the task of finding an exposition which, based on a unified approach, ensures the possibility of applying the theory in other natural sciences, since it provides a simple and effective method for the independent solution of problems that arise in practice in physics, engineering and mathematics.Foundations of the theory of special functions
The classical orthogonal polynomials
Bessel functions
Hypergeometric functions
Solution of some problems of mathematical physics, quantum mechanics and numerical analysis