#3236 bug in simplifying infinite sum with 1st (0th) negative term

[Dima Pasechnik]

the 1st term (for n=0) of sum(1/((n+1)(2n-1)), n, 0,inf) is -1, the rest are positive. However:

(%i42) bfloat(simplify_sum(sum(1/((n+1)*(2*n-1)), n, 1,inf))
  -simplify_sum(sum(1/((n+1)*(2*n-1)), n, 0,inf)));

(%o42)                        1.888888888888889b0

instead of 1.0 (one can also see this symbolically, it outputs an expression off by a rational number).

This is checked with Maxima 5.38.1 complied with SBCL, as well as with ECL.

[Robert Dodier]

+tags; formatting

[Andrej Vodopivec]

Fixed with commit 989086adeb0b5dd72b3e809edc36a30c976ca3ba

[Dima Pasechnik]

Thanks.
Why are you commending out things, rather than removing them?
(isn't it what git is for, to make such poor man's way of version control unnecessary?)

[Dima Pasechnik]

this patch breaks the following (at least on 5.38.1 with ECL):

simplify_sum(sum(1/((2*n-1)^2*(2*n+1)^2*(2*n+3)^2), n, 0, inf));

which should be 3/256pi^2, and not 3/256pi^2 - 1/32, as I get after the patch is applied.

Please re-open.

[Dima Pasechnik]

IMHO, these two examples ought to make it into Maxima's testsuite.

[Andrej Vodopivec]

Both sums are computed correctly after commit 8ec3a05cd24c756f29e0501488be971fe13f7c1f

[kcrisman]

Does this also cover

(%i11) display2d:false;

(%o11) false
(%i12) simplify_sum(sum(1/((2*n+1)^2-4)^2, n, 0, inf));

(%o12) (14/3-2*log(2))/64-(2-2*log(2))/64+(%pi^2/2-4)/32

where the answer apparently should be 1/64%pi^2 (see https://ask.sagemath.org/question/35839/sage-incorrectly-evaluates-series/ )?

[Robert Dodier]

With current source code, and using Clisp and ECL, I get 1/64*%pi^2 as expected. Are you sure you are getting a different result? If so, is it perhaps an interaction with some flags that Sage is setting?

[Dima Pasechnik]

I presume Karl-Dieter talks about an old Maxima version (5.35).

[kcrisman]

I hope so, yes! In fact perhaps this commit fixed this bug - I just wasn't able to check.