Mathematica Cannot do the integral of the Hyper-geometric function?

AI Thread Summary
The discussion centers around the evaluation of two integrals involving the hypergeometric function, specifically comparing the integrals of ##\int_0^\infty dx~x~_2F_1(a,b,c,1-x^2)## and ##\int_0^\infty dx~x~_2F_1(a,b,c,1-x-x^2)##. It is noted that Mathematica successfully computes the first integral but fails with the second. Participants express skepticism about the possibility of an analytical solution for the second integral, suggesting that resources like Rydzik and Gradshteyn may provide insights or alternative approaches. The conversation emphasizes the complexity of the second integral and the potential need for specialized references to explore its evaluation.
Chenkb
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Dear friends:
It's strange that Mathematica can do the integral of ##\int_0^\infty dx~x~_2F_1(a,b,c,1-x^2)##, however, fails when it's changed to ##\int_0^\infty dx~x~_2F_1(a,b,c,1-x-x^2)##.
Are there any major differences between this two types? Is it possible to do the second kind of integral?
Best regards!

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I don't believe that that particular integral can be solved analytically. Best place to look is in Rydzik and Gradstien (sp)...
 
Dr Transport said:
I don't believe that that particular integral can be solved analytically. Best place to look is in Rydzik and Gradstien (sp)...
Many thanks! That reference is excellent!
 

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