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).