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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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    (http://dlmf.nist.gov/) – 2017-02-03
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    NIST has produced a wonderfully illustrated book (https://www.amazon.com/Handbook-Mathematical-Functions-Paperback-CD-ROM/dp/0521140633) that I recommend you as very appealing. – 2017-02-03
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    The handbook in the link can be good for your needs. http://people.math.sfu.ca/~cbm/aands/abramowitz_and_stegun.pdf – 2017-02-03
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    Related: http://math.stackexchange.com/questions/759377/reference-book-on-special-functions, http://math.stackexchange.com/questions/1639809/book-recommendation-on-special-functions, http://math.stackexchange.com/questions/2032855/books-about-special-functions-in-physics, http://math.stackexchange.com/questions/405383/can-you-recommend-some-books-on-elliptic-function. – 2017-02-03
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    @Mathlover Good to know that there is an online version of this reference book, which is always invaluable for people that are far from university resources. This book is so splendidly organized with all the essential that it is still advisable. The lack of internet references/connexions is the increasing tribute to pay to all the scientific work before 2000. – 2017-02-03
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    @JeanMarie It is also good that I just searched "handbook mathematical functions" and first link was this book as pdf. As you said what a great opportunity for developing of Mathematics that everybody can reach with simple search – 2017-02-03

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