## #8582 closed defect (fixed)

# sum(1/(1+k^2), k, -oo, oo) returns 0

Reported by: | Minh Van Nguyen | Owned by: | Burcin Erocal |
---|---|---|---|

Priority: | major | Milestone: | sage-4.6.1 |

Component: | symbolics | Keywords: | |

Cc: | Merged in: | ||

Authors: | Reviewers: | ||

Report Upstream: | N/A | Work issues: | |

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description

From sage-support:

But I want to make a comment, also from this documentation. It says sum(1/(1+k^2), k, -oo, oo, algorithm = 'mathematica') # optional -- requires mathematica OK, I understand that sage do not kown how to evaluate sum(1/(1+k^2), k, -oo, oo) But it answer 0 , that is wrong!!!

### Change History (6)

### comment:1 Changed 12 years ago by

### comment:3 Changed 12 years ago by

Resolution: | → fixed |
---|---|

Status: | new → closed |

This is fixed at ticket #10187 by upgrading to Maxima 5.22.1:

[mvngu@sage sage-4.6.1.alpha3]$ ./sage ---------------------------------------------------------------------- | Sage Version 4.6.1.alpha3, Release Date: 2010-12-05 | | Type notebook() for the GUI, and license() for information. | ---------------------------------------------------------------------- ********************************************************************** * * * Warning: this is a prerelease version, and it may be unstable. * * * ********************************************************************** sage: k = var("k") sage: sum(1/(1+k^2), k, -oo, oo) 1/2*I*psi(-I) - 1/2*I*psi(I) + 1/2*I*psi(-I + 1) - 1/2*I*psi(I + 1) sage: %maxima --> Switching to Maxima <-- '' maxima: load(simplify_sum); "/dev/shm/mvngu/sage-4.6.1.alpha3/local/share/maxima/5.22.1/share/contrib/solve_rec/simplify_sum.mac" maxima: display2d:false; false maxima: maxima: simplify_sum(sum(1/(1+k^2),k,-inf,inf)); -%i*(psi[0](%i+1)+%gamma)/2-%i*(psi[0](%i)+%gamma)/2+%i*(psi[0](-%i)+%gamma)/2+%i*(psi[0](1-%i)+%gamma)/2

So I'm closing this ticket as fixed.

### comment:5 Changed 12 years ago by

Replying to kcrisman:

Is that doctested in the patches for #10187?

No. But it shouldn't be difficult to write a documentation patch with doctests in the current ticket. The Sage 4.6.1 release cycle is now in feature freeze, but I think documentation patches are OK for merging in the upcoming release candidates.

**Note:**See TracTickets for help on using tickets.

This seems to be fixed in Maxima 5.21.1 or so:

Which uses the digamma function quite a bit. We don't get the (perhaps) simpler answer

`pi coth(pi)`

.