# Book on gamma functions with applications in Quantum Mech.

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1. Sep 20, 2015

### Joker93

I have heard that in my next semester, our quantum mechanics teacher will be giving a great emphasis on difficult integrals with the most of them having to do with gamma functions.

Does anybody know a book(or any other source) that I can learn about and practice gamma functions integration (with applications to physics and more preferably quantum mechanics if possible)?

The only thing I have found are books that just list the integrals of gamma functions in tables rather than having a few examples and them some practice problems.

Thank you!

2. Sep 20, 2015

### Anama Skout

Here are some references I found out on reddit: (I don't know if that's advanced enough for your level)

Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals
, by George Boros and Victor Moll.
Chapter 11 deals with the Gamma and Beta functions.

Paul Nahin, Inside Interesting Integrals.
Pages 117-147 deals with the Gamma and Beta functions.

Special Integrals of Gradshteyn and Ryzhik: the Proofs - Volume I
by Victor H. Moll

has a section providing proofs of formulas in Gradshteyn and Ryzhik. (I'm not sure if anyone of them has applications in QM)

3. Sep 21, 2015

### Joker93

Thanks for the recommendations. I already know about Nahin's awesome book and I also know that it has some applications.

4. Sep 22, 2015

### vanhees71

5. Sep 22, 2015

### Anama Skout

Also anhttp://www.uni-graz.at/~gronau/TMCS_1_2003.pdf [Broken] that attempts to answer: "Why is $\Gamma(n)=(n-1)!$ and not $\Gamma(n)=n!$?"

Edit: Some other papers:
• Wladimir de Azevedo Pribitkin, Laplace's Integral, the Gamma Function, and beyond, American Mathematical Monthly.
• Gopala Krishna Srinivasan, The Gamma Function: An Eclectic Tour, American Mathematical Monthly.
• Dorin Ervin Dutkay, Constantin P. Niculescu, Florin Popovici, Stirling’s Formula and Its Extension for the Gamma Function, American Mathematical Monthly.

Last edited by a moderator: May 7, 2017