On 5/06/2012 7:24 AM, Stavros Macrakis wrote:
> load(simplify_sum)$
> simplify_sum(...)
>
> Unfortunately, in your case, simplify_sum gives the result as the
> hypergeometric function %f[0,2]([],[1/3,2/3],x^3/27), which may be
> correct, but isn't very helpful.
>
> Similarly, simplify_sum( sum( (-1)^n*x^(2*n)/(2*n)!, n,0,inf ) )
> gives sqrt(%pi)*bessel_j(-1/2,x)*sqrt(x)/sqrt(2) rather than
> cos(x).... Correct, but not as nice.
>
... and using using besselexpand:true
(%i5) load(simplify_sum)$
(%i6) simplify_sum( sum( (-1)^n*x^(2*n)/(2*n)!, n,0,inf ) );
(%o6) sqrt(%pi)*bessel_j(-1/2,x)*sqrt(x)/sqrt(2)
(%i7) %,besselexpand:true;
(%o7) cos(x)