Timeline for Singularity structure of integrals of rational functions
Current License: CC BY-SA 4.0
15 events
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| May 26, 2018 at 18:43 | comment | added | j.c. | @fedja Thanks! This is more than sufficient for my curiosity. | |
| May 26, 2018 at 3:04 | comment | added | fedja | @j.c. Now I reduced it to a few one-dimensional integrals . Are you interested in seeing those or it already qualifies as "a sketch"? | |
| May 24, 2018 at 0:24 | answer | added | fedja | timeline score: 4 | |
| May 22, 2018 at 23:34 | comment | added | fedja | @j.c. OK, I'll post in small morsels as usual, when I have some time for typing :-) | |
| May 22, 2018 at 9:11 | comment | added | j.c. | @fedja I for one would be curious to see a sketch, if it's not too much trouble. | |
| May 20, 2018 at 18:47 | comment | added | fedja | What you ask for can be done for this particular integral (no systematic approach though, just some combination of trickery and luck) except $\log^2 c$ appears in the quadratic part as well. Let me know if you are still interested after 7 years (if you aren't, I'd rather spare a couple of hours of typing). | |
| May 20, 2018 at 16:32 | comment | added | fedja | The back of envelope computation (no rigor!) suggests that even the leading singularity is some constant times $\log a\log b\log c+\frac 12(\log a+\log b)\log^2 c+\frac 13\log^3 c$. To extract the lower order terms may be a real headache (alas, I don't know any systematic way of doing that). What is the minimal information you can get away with? | |
| May 20, 2018 at 15:45 | comment | added | j.c. | @AlexM. The "Feynman integral" that you refer to is the Feynman path integral. By "Feynman integral" in his edit, David S-D means an integral arising from the evaluation of a Feynman diagram (which are related, as they appear in perturbative calculations of path integrals). See en.wikipedia.org/wiki/Feynman_diagram and en.wikipedia.org/wiki/Feynman_parametrization | |
| May 20, 2018 at 15:17 | comment | added | Alex M. | The Feynman integral is a hypothetical integral that should allow one to integrate over spaces of curves, very similar to the Wiener measure - the formal difference being that the "time parameter" is multiplied by a $\sqrt {-1}$. How is your integral an instance of a Feynman integral? | |
| May 20, 2018 at 15:06 | history | edited | David S-D | CC BY-SA 4.0 |
Added tag suggested by reviewer. Clarified that example integral is a Feynman integral.
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| S May 20, 2018 at 15:04 | history | rollback | David S-D |
Rollback to Revision 2 - Edit approval overridden by post owner or moderator
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| May 14, 2018 at 14:43 | history | suggested | Alex M. |
Changed tags: the question has nothing to do with Feynman integrals; added a top-level tag
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| May 14, 2018 at 13:43 | review | Suggested edits | |||
| S May 20, 2018 at 15:04 | |||||
| May 14, 2018 at 12:12 | history | edited | j.c. |
add tag
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| Feb 25, 2011 at 3:45 | history | asked | David S-D | CC BY-SA 2.5 |