Book on gamma functions with applications in Quantum Mech.

[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!

 

[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.

6.4 of Gradshteyn and Ryzhik are about the Gamma function, and

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)

 

[Joker93]

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.

6.4 of Gradshteyn and Ryzhik are about the Gamma function, and

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)

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

 

[vanhees71]

Perhaps also my lecture notes on QFT are of use here. There's a section on the $\Gamma$ function and a chapter on dim. reg. where it is used heavily:

http://fias.uni-frankfurt.de/~hees/publ/lect.pdf

 

[Anama Skout]

Also anhttp://www.uni-graz.at/~gronau/TMCS_1_2003.pdf 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.