Sage incorrectly evaluates series

answered 2016-12-01 12:57:01 +0200

Sébastien
3153 ●5 ●39 ●85 http://www.slabbe.org/

updated 2016-12-01 13:25:10 +0200

Indeed:

sage: n = var('n')
sage: sum(1/((2*n+1)^2-4)^2, n, 0, Infinity)
1/64*pi^2 - 1/12

See ticket #22005. Mathematica does it correctly:

sage: sum(1/((2*n+1)^2-4)^2, n, 0, Infinity, algorithm='mathematica')
1/64*pi^2

Giac gives this:

sage: sum(1/((2*n+1)^2-4)^2, n, 0, Infinity, algorithm='giac')
1/32*Psi(-1/2, 1) - 1/8

And SymPy seems to do it correctly:

sage: from sympy.abc import n
sage: from sympy import summation, oo
sage: A = summation(1/((2*n+1)^2-4)^2, (n, 0, oo))
sage: A._sage_()
1/64*pi^2

I created ticket #22004 so that one can do:

sage: sum(1/((2*n+1)^2-4)^2, n, 0, Infinity, algorithm='sympy')
1/64*pi^2

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Thanks! We should also file an upstream bug report at Maxima - can you do that as well?

kcrisman ( 2016-12-01 13:26:30 +0200 )edit

I do not not have a account on the sourgeforge of maxima. Also I do not have access to version latest version 5.38. If possible, I will let somebody else do the upstream bug report.

Sébastien ( 2016-12-01 13:55:09 +0200 )edit

Thanks for the ticket !

tmonteil ( 2016-12-01 14:59:13 +0200 )edit

This may actually be https://sourceforge.net/p/maxima/bugs... which is apparently fixed in upstream.

kcrisman ( 2016-12-01 15:04:19 +0200 )edit

I've got ValueError: Mathematica cannot make sense of input sum(1/((2*x+1)^2-4)^2,x,0,Infinity, algorithm='mathematica')

proy87 ( 2016-12-01 16:11:02 +0200 )edit

I confirm that for me it works:

sage: x = var('x')
sage: sum(1/((2*x+1)^2-4)^2,x,0,Infinity, algorithm='mathematica')
1/64*pi^2

with this version:

sage: mathematica_console()
Mathematica 10.0 for Linux x86 (64-bit)
Copyright 1988-2014 Wolfram Research, Inc.

Sébastien ( 2016-12-01 16:26:26 +0200 )edit

OK. Thank you.

proy87 ( 2016-12-01 17:48:17 +0200 )edit

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