Timeline for Closed formula for reversion of Jacobi theta series
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Jul 7, 2021 at 9:08 | vote | accept | user70925 | ||
| Jul 6, 2021 at 14:32 | comment | added | Max Alekseyev | @PeterTaylor: Indeed, I was about to make the same correction :) | |
| Jul 6, 2021 at 14:30 | comment | added | Peter Taylor | @MaxAlekseyev, oh dear, I have made a mess of that comment. I copied the wrong part of my workings out: it should read $3s + 8t + 15u + 24v + \cdots = n-1$. | |
| Jul 6, 2021 at 12:16 | answer | added | Max Alekseyev | timeline score: 3 | |
| Jul 6, 2021 at 11:54 | history | edited | user70925 | CC BY-SA 4.0 |
edited title
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| Jul 6, 2021 at 10:13 | comment | added | Peter Taylor | Apologies, I seem to have lost a reciprocal along the way. Change $n2^{-n}$ to $n^{-1} 2^{-n}$. | |
| Jul 6, 2021 at 9:18 | comment | added | მამუკა ჯიბლაძე | To avoid confusion it would be better to call it reversion rather than inversion (the latter can be more likely understood as multiplicative inverse). | |
| Jul 6, 2021 at 7:47 | comment | added | Peter Taylor | With a bit of simplification, $$A_n = n2^{-n} \sum_{s,t,u,\ldots} (-1)^{s+t+u+\cdots} \binom{n-1+s+t+u+\cdots}{s,t,u,\ldots}$$ where the sum is over non-negative integer solutions to $s + 2t + 3u + \cdots = n-1$. | |
| Jul 6, 2021 at 7:38 | comment | added | Peter Taylor | Morse-Feshbach (see bottom of page) gives a sum over partitions of $n-1$ into numbers one less than a square; it's not a closed form or an elegant recurrence, but if your concern is practical evaluation then it may be of interest. | |
| Jul 6, 2021 at 7:36 | history | edited | user70925 | CC BY-SA 4.0 |
added 33 characters in body
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| Jul 6, 2021 at 7:35 | comment | added | user70925 | Yes, indeed, it's exactly the same problem. | |
| S Jul 6, 2021 at 1:49 | history | suggested | Somos | CC BY-SA 4.0 |
Fixed obvious typo.
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| Jul 6, 2021 at 1:29 | review | Suggested edits | |||
| S Jul 6, 2021 at 1:49 | |||||
| Jul 5, 2021 at 18:00 | comment | added | F. C. | By closely related, one should understand related by the substitution $q \mapsto q/2$. | |
| Jul 5, 2021 at 17:06 | history | asked | user70925 | CC BY-SA 4.0 |