maxima sum returns hypergeometric function

[haraldschilly]

The parsing of Maxima's output is not good enough to handle this:

var('n')
sum(((2*I)^n/(n^3+1)*(1/4)^n), n, 0, infinity)

gives an exception

TypeError: unable to make sense of Maxima expression 'f[4,3]([1,1,-(sqrt(3)*I+1)/2,(sqrt(3)*I-1)/2],[2,-(sqrt(3)*I-1)/2,(sqrt(3)*I+1)/2],I/2)' in Sage

which is - i think - a f_43 hypergeometric function.

CC: @eviatarbach

Component: symbolics

Keywords: hypergeometric

Reviewer: Karl-Dieter Crisman, Ralf Stephan

Issue created by migration from https://trac.sagemath.org/ticket/9908

[haraldschilly]

comment:1

one additional example by omologos on irc:

var('x n')
f=(-1)^n/((2*n+1)*factorial(2n+1))
sum(f,n,0,oo)

but i get this error:

TypeError: unable to make sense of Maxima expression 'f[1,2]([1/2],[3/2,3/2],-1/4)' in Sage

[kcrisman]

comment:2

This should be

var('x n')
f=(-1)^n/((2*n+1)*factorial(2*n+1))
sum(f,n,0,oo)

If I'm not mistaken, this might be related to #2516, in the sense that we should be parsing hypergeometric functions correctly and that would be part of that ticket.

[eviatarbach]

comment:4

This also causes a similar problem in #4102:

sage: f = bessel_J(2, x)
sage: f.integrate(x)
Traceback (most recent call last):
...
TypeError: cannot coerce arguments: no canonical coercion from <type 'list'> to Symbolic Ring

In that case, Maxima is returning hypergeometric([3/2],[5/2,3],-x^2/4).

[kcrisman]

comment:6

See also http://ask.sagemath.org/question/3091 for another example.

[fchapoton]

Changed keywords from none to hypergeometric

[kcrisman]

comment:9

And see this sage-support thread for possibly another example.