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.

[kcrisman]

comment:11

#2516 has all the examples above in it, with the exception of the ones mentioned in the comments.

• One would want to be able to do

b=var('b')
integral(1/(x^b+1),x)

without using W|A; apparently 1/(a^b+1) would yield 2F1(1,1/a,1+1/a,-a^x).

• Apparently

sum(x^(3*k)/factorial(2*k),k,0,oo)

would also be doable with hypergeometrics.

[rwst]

comment:12

Replying to @kcrisman:

#2516 has all the examples above in it, with the exception of the ones mentioned in the comments.

What I get with #2516 is

sage: integral(1/(x^b+1),x)
integrate(1/(x^b + 1), x)
sage: sum(x^(3*k)/factorial(2*k),k,0,oo)
sqrt(pi)*x^(3/4)*sqrt(1/(pi*x^(3/2)))*cosh(x^(3/2))

[kcrisman]

comment:13

What I get with #2516 is

sage: integral(1/(x^b+1),x)
integrate(1/(x^b + 1), x)

Not really worth keeping open, as even Maxima does this.

sage: sum(x^(3*k)/factorial(2*k),k,0,oo)
sqrt(pi)*x^(3/4)*sqrt(1/(pi*x^(3/2)))*cosh(x^(3/2))

Interestingly, this works in vanilla Sage as well. Maybe there weren't any hg functions to begin with there. I assume it was fixed with #16224 - earlier it gave yet another (wrong) answer.

So I nominate to close this ticket.

[kcrisman]

Reviewer: Karl-Dieter Crisman, Ralf Stephan

[kcrisman]

comment:14

sage: sum(x^(3*k)/factorial(2*k),k,0,oo)
sqrt(pi)*x^(3/4)*sqrt(1/(pi*x^(3/2)))*cosh(x^(3/2))

Interestingly, this works in vanilla Sage as well. Maybe there weren't any hg functions to begin with there. I assume it was fixed with #16224 - earlier it gave yet another (wrong) answer.

Even more interestingly, this is not as simple as just cosh(x^(3/2)) (which is correct) but I'm not going to repurpose this one for that.

[rwst]

comment:15

Practically a duplicate of #2516