Luke Y. The Special Functions and Their Approximations Vol 1-2. 1969

Textbook in PDF format

These volumes are designed to provide scientific workers with a self-contained and unified development for many of the mathematical functions which arise in applied problems, as well as the attendant mathematical theory for their approximations. These functions are often called the special functions of mathematical physics or more simply the special functions.
Although the subject of special functions has a long and varied history, we make no attempt to delve into the many particulars of Bessel functions, Legendre functions, incomplete gamma functions, confluent hypergeometric functions, etc., as these data are available in several sources. We have attempted to give a detailed treatment of the subject on a broad scale on the basis of which many common particulars of the above-named functions, as well as of others, can be derived. Hitherto, much of the material upon which the volumes are based has been available only in papers scattered throughout the literature