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)