the bound are from 0 to infinity but i mostly would like to know how to go about this integral.

Thank you

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- April 29th 2010, 08:37 AMankuoliTough integral
the bound are from 0 to infinity but i mostly would like to know how to go about this integral.

Thank you - April 29th 2010, 08:47 AMChris L T521
- April 29th 2010, 08:59 AMkompik
To make things simpler, I will assume .

Integration by parts gives:

So I think, that with some effort you can express it using Phi-function or some of the related functions, but you cannot expect a closed form using only elementary functions.

(I hope I haven't made some embarrassing error in the calculation - but plenty of attentive eyes are here, ready to spot any mistake.) - April 29th 2010, 09:02 AMChris L T521
- April 29th 2010, 09:34 AMkompik
- April 29th 2010, 09:37 AMankuoli
i have not done integration by parts or substitution in a very long time, so i'm a bit stuck. But i do like the idea of the gamma function. Any help on substitution to get started would be great.

thanks - April 29th 2010, 09:40 AMkompik
- April 29th 2010, 10:01 AMankuoli
Do i then have dv= and v=

and then do uv- ???

Also to add to the fun of this problem:

I know that the distribution of is an

and the whole integral is .

Ideally I would like this integral to equal 1/2 but i have a feeling it's not going to happen. - April 29th 2010, 10:07 AMkompik
- April 29th 2010, 10:21 AMankuoli
so how exactly do i use u in the gamma function? sorry i'm very confused

- April 29th 2010, 10:23 AMkompik
Good start to learn the basics about this function could be wikipedia.