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The hypergemoetric function $_2F_1(a,b,c,z)$ happens to be the primitive of a well known function in astroparticle physics. Result integration by WolframAlpha

In my work, this object is part of more complex function, which is minimized by varying the values of the parameters $a,b,c$.

The question is: for $z<0$, what are the bounds on the parameters $a,b,c$ for $_2F_1(a,b,c,z)$ to be positive definite? Thank you very much for your comments and help.

andrea
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  • Nothing? I realise that, perhaps, it's not a standard mathematical question, but I would just need a pointer to some paper or web page which addresses my query or where I could find hints. Thank you – andrea Dec 07 '16 at 09:34
  • At the least, the hypergeometric function will be positive definite for all $0\le b\le c$. This is obvious from the integral representation. – David H Dec 15 '16 at 05:45

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