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Book on gamma functions with applications in Quantum Mech.

  1. Sep 20, 2015 #1
    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. jcsd
  3. Sep 20, 2015 #2
    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)
     
  4. Sep 21, 2015 #3
    Thanks for the recommendations. I already know about Nahin's awesome book and I also know that it has some applications.
     
  5. Sep 22, 2015 #4

    vanhees71

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  6. Sep 22, 2015 #5
    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
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