- #1
bruno67
- 32
- 0
I am trying to calculate the following integral
[tex]I=\int_0^\infty\frac{x}{(x+ia)^2} {\mbox{$_2$F$_1\!$}}\left(\frac{1}{2},b,\frac{3}{2},-\frac{x^2}{c^2}\right) dx.
[/tex]
I tried several different ways but drew a complete blank. Is there a way of converting this nasty hypergeometric function into something which is more tractable? Unfortunately the definition of the hypergeometric function as a series cannot be used, since it is only valid when the fourth argument is less than 1 in modulus.
Thanks.
[tex]I=\int_0^\infty\frac{x}{(x+ia)^2} {\mbox{$_2$F$_1\!$}}\left(\frac{1}{2},b,\frac{3}{2},-\frac{x^2}{c^2}\right) dx.
[/tex]
I tried several different ways but drew a complete blank. Is there a way of converting this nasty hypergeometric function into something which is more tractable? Unfortunately the definition of the hypergeometric function as a series cannot be used, since it is only valid when the fourth argument is less than 1 in modulus.
Thanks.