Comprehensive compendia of mathematical properties of the special functions are provided by the National Bureau of Standards' Handbook of Mathematical Functions [AS64], published originally in 1964, and the 3-volume set that resulted from the Bateman Manuscript Project [EMOT53a,EMOT53b,EMOT55], published in 1953 and 1955. These references employ the same notation for the special functions, and we shall follow them. The NBS Handbook has been reprinted many times by the U. S. Government Printing Office and has also been issued in whole, or in part, by other publishers including Dover Publications, Moscow Nauka, Verlag Harri Deutsch and Wiley-Interscience.
The forerunner of [AS64] is the book of Jahnke and Emde [JE45], published originally in 1909, and still in print8. It continues to be useful, especially for its collection of graphs. Other useful compendia include those of Magnus, Oberhettinger and Soni [MOS66], and (from the standpoint of hypergeometric functions) Luke [Luk69a]. For an introductory compendium, see the recent ``atlas'' of Spanier and Oldham [SO87].
Books and articles that include descriptions or surveys of general methods for computing special functions include [Bre78b,DKK81,Gau75,HCL+68,Luk69b,Luk77b,PT84,PTVF92,Tem78,vdLT84].
Other books and articles that provide indepth coverage of pertinent topics include:
[Ask89, survey of compendia], [BG81a,BG81b, Padé approximations], [BH75, asymptotic approximations], [Bre91, continued fractions, Padé approximations], [BvI93, Padé approximations], [Cod70, polynomial and rational approximations], [Fik68, polynomial and rational approximations], [FP68, Chebyshev polynomials], [JT80, continued fractions], [Kar91, power series], [KG80, statistical computations], [Luk75, supplement to AS64--especially for functions of hypergeometric type], [Mor80, power series], [Olv74, asymptotic approximations], [Riv90, Chebyshev polynomials], [Tem77, integral representations], [Tem85, asymptotic approximations], [Wim84, recurrence relations], [Won89, asymptotic approximations].