>
> But other sums are simply wrong.
>
> k = var('k')
> sum(x^(2*k)/factorial(2*k),k,0,oo)
>
> gives
>
> -1/4*sqrt(2)*sqrt(pi)*x^(3/2)
>
> but the answer should be sinh(x).
>
>
Hmm. That shouldn't be happening, though I wouldn't be surprised if it
didn't turn out as easy as that.
(%i1) load(simplify_sum);
(%o1) /Users/.../Sage-5.12-OSX-64bit-10.6.app/Contents/Reso\
urces/sage/local/share/maxima/5.29.1/share/solve_rec/simplify_sum.mac
(%i3) display2d:false;
(%o3) false
(%i4) simplify_sum(sum(x^(2*k)/factorial(2*k),k,0,inf));
(%o4) sqrt(%pi)*bessel_i(-1/2,x)*sqrt(x)/sqrt(2)
So I'm not sure why that would happen - maybe because of incorrect Bessel
simplification?
sage: maxima_calculus('bessel_i(-1/2,x)')
bessel_i(-1/2,x)
sage: _._sage_()
sqrt(2)*sqrt(1/(pi*x))*cosh(x)
That gives cosh(x), which I think is what you meant. This is now tracked
at http://trac.sagemath.org/ticket/16224.
> For other sums, Sage simply repeats what I told it.
>
> sum(x^(3*k)/factorial(2*k),k,0,oo)
>
> I understand that Sage has limited exploitation of Maxima's hypergeometric
> functionality, and I suspect this is the main issue. Are there any
> conceivable workarounds?
>
>
Yeah, that is definitely part of it. See e.g
http://trac.sagemath.org/ticket/9908 .
- kcrisman
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