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Hypergeometric transformations and identities

  1. Feb 28, 2007 #1
    How do you derive hypergeometirc identities of the form

    2F1(a,b,c,z)= gamma function. What I mean is that the hypergeometric function converges to a set of gamme functions function in terms of (a,b,c)

    where z is not 1,-1, or 1/2 ?

    The hypergeometric identities in the mathworld summary which give gamma functions only have values of 1,-1, and 1/2 for Z but none others.

    I have seen hypergeometric functions where z=1/8,1/3, 2/3 etc that give gamma functions but have no idea how to deive them despite many months of time and research.
     
  2. jcsd
  3. Mar 2, 2007 #2
    After spending another 3 days with the problem I used a kummer quadratic identity combined with annother kummer transformation to get a hypergeometric function for z=-1/8

    [​IMG]

    (8^(-3b+1)/2)*2F1((3b-1)/2,-b/2+1/2;1/2+b;-1/8)=

    4*(gammafunction(1/2)*gammafunction(2b))/(b*gammafunction(b/2))^2

    there are more possible
     
    Last edited: Mar 2, 2007
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