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Where can I find the definitions of the special functions?

Posted 10 years ago

In my work, I deal with special functions on a daily basis. These include different types of Legendre functions, both P-functions and Q-functions, as well as Gegenbauer functions. The problem arises from the disparate definitions of these functions that we can find in various different sources. I've learned that Mathematica classifies Legendre P-functions in three different varieties according to the branch cut. Now I'm trying to establish a connection between the different Legendre functions in Mathematica, and those that I can find in literature, such as in Handbook of Mathematical Functions by Abramowitz and Stegun and NIST Digital Library of Mathematical Functions. It seems that there is no exact one-to-one correspondence between the Mathamatica functions and the ones outlined in the two handbooks. If someone could point out a handbook that deals with the Mathematica versions of special functions, the would be greatly appreciated.

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