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Can any of you suggest any basic reference mainly focused on special functions/no elementary functions. I'm not familiar with them (except for sparse reference that involve those functions).

I'm talking of stuff like Bessel functions, elliptic integrals, gamma functions etc.

I'd like to find some reference that explains the properties of such functions (maybe with related proofs)

Thx

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Here is some references mainly focused on special functions, I think it will help you a lot.

$1.~~$ "Special functions and their applications" by N. N. Lebedev, Richard A. Silverman

$2.~~$ "Special Functions for Scientists and Engineers" by W. Bell

$3.~~$ "Special Functions: An Introduction to the Classical Functions of Mathematical Physics" by Nico M. Temme

$4.~~$ "Special Functions" by George E. Andrews, Richard Askey, Ranjan Roy

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