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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: 1,036
Registered: 5/5/07
Re: integral for fun
Posted: Mar 1, 2014 11:21 AM
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On 01.03.2014 12:12, Axel Vogt wrote:
> 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)


Typo: read as "where 'a' runs through the four solutions of z^4 + 1 = 0"
(and one can replace "-a" by "a" in the final formula).





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