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Unexpected result for the sum of a series

asked 2012-11-15 02:48:43 +0200

Pierre-Yves Gaillard gravatar image

updated 2023-01-10 01:57:41 +0200

tmonteil gravatar image

I typed

n = var('n')

sum(1/((2*n-1)^2*(2*n+1)^2*(2*n+3)^2), n, 0, oo)

sage answered

3/256*pi^2 - 1/32

By hand computation (via Fourier series), and by WolframAlpha I got



Link to WolframAlpha's result.

(This is my first question. If it is inappropriate here, please tell me where I should ask it. I used the tag "bug", but I of course mean "potential bug". Thank you very much in advance!)

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answered 2012-11-15 06:39:42 +0200

This is a bug. It is now #13712 on the Sage issue tracker.

Sage calls Maxima to evaluate symbolic sums. Somebody will have to pass the report upstream to the Maxima developers.

Thanks for your report.

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This has been reported upstream at [Maxima artifact 3587514](

kcrisman gravatar imagekcrisman ( 2012-11-15 08:55:38 +0200 )edit

answered 2023-01-10 01:57:20 +0200

tmonteil gravatar image

This bug is fixed:

sage: n = var('n')
....: sum(1/((2*n-1)^2*(2*n+1)^2*(2*n+3)^2), n, 0, oo)

Setting tags from confirmed_issue to fixed_issue.

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Asked: 2012-11-15 02:48:43 +0200

Seen: 647 times

Last updated: Jan 10 '23