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Topic: integral for fun
Replies: 25   Last Post: Mar 6, 2014 4:10 PM

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Axel Vogt

Posts: 1,040
Registered: 5/5/07
Re: integral for fun
Posted: Mar 1, 2014 6:12 AM
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On 01.03.2014 05:33, Richard Fateman wrote:
> I don't consider a solution that includes
> Si, Ci, or hypergeometric functions as a solution
> in closed form in terms of elementary functions.
>
> Unless there is no way of expressing the answer in
> terms of elementary functions.

...

Using Cosinus Fourier one can achieve it in terms of elementary functions.

F:= (a,t) -> -1/8*Pi*a/sqrt(-a)*exp(-sqrt(-a)*t), the transform of a/(a-x^2)/4

Then it is 2*Sum( F(a, 4)/8 + F(a, 2)/2 + F(a, 0)*3/8), a),
where 'a' runs through the four solutions of z^2+1 = 0.

Or more nicely: Pi/32*Sum((exp(-4*sqrt(-a))+4*exp(-2*sqrt(-a))+3)*sqrt(-a), a)





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