Timeline for What partial sum formulae exist for this basic hypergeometric series?
Current License: CC BY-SA 4.0
26 events
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| Jan 26, 2019 at 19:02 | answer | added | Sotiris | timeline score: 1 | |
| Jan 26, 2019 at 18:47 | history | edited | user3108815 | CC BY-SA 4.0 |
edited title
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| Jan 26, 2019 at 17:32 | history | edited | user3108815 | CC BY-SA 4.0 |
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| Jan 26, 2019 at 17:21 | comment | added | user3108815 | @Linas I looked at the book "A=B" for inspiration there. | |
| Jan 26, 2019 at 17:20 | history | edited | user3108815 | CC BY-SA 4.0 |
added 182 characters in body; edited title
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| Jan 26, 2019 at 17:06 | history | edited | user3108815 | CC BY-SA 4.0 |
Edited to reflect LInas' point about extracting a partial sum formula
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| Jan 26, 2019 at 7:38 | answer | added | Linas | timeline score: 1 | |
| Jan 26, 2019 at 7:15 | comment | added | Linas | re: basic hypergeometric: what the wikipedia article does not say is that there are an infinite number of crazy identities connecting them all, and modern research on them is focused on finding algos that are able to list & classify the identities. I think Adamchick does this if I recall. But with a finite sum, I'm not clear on what you can do, or what you hope to get. | |
| Jan 26, 2019 at 7:08 | comment | added | Linas | I don't know what you mean by a "partial sum". If this was an infinite series, you could almost surely re-write it in terms zetas (hurwitz or lerch), gammas and digammas, thetas or mock theta, binomial coefficients and stirling numbers and ascending or descending pochammers. Apply a dirichlet convolution to remove the denominator. There;'s almost an infinite number of these, limited by your creativity. But none of these kinds of rewrites make it simpler or "closed"; they just create lots of fun-looking identities. | |
| Jan 25, 2019 at 21:55 | history | edited | user3108815 | CC BY-SA 4.0 |
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| Jan 25, 2019 at 17:00 | history | edited | user3108815 | CC BY-SA 4.0 |
Added some links for background
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| Jan 25, 2019 at 7:02 | comment | added | user3108815 | @DavidRoberts Fixed the uncomfortable portions! | |
| Jan 25, 2019 at 7:02 | history | edited | user3108815 | CC BY-SA 4.0 |
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| Jan 25, 2019 at 6:56 | comment | added | David Roberts♦ | @user3108815 it was meant to be a joke: is $\mathbb Q <1$ ? :-) Why not $q\in (0,1)$? Is there something special about rational $q$? Why not just say in the text after the displayed equation that "where $q$ is an integer greater than 1 or a rational number in $(0,1)$"? | |
| Jan 25, 2019 at 6:38 | comment | added | user3108815 | @DavidRoberts The intention was not to trigger you, I apologize. Can you (please) suggest the proper notation to express what is already intended to be expressed? | |
| Jan 25, 2019 at 5:08 | comment | added | David Roberts♦ | $0 \lt q \in \mathbb Q \lt 1$ [triggered] | |
| Jan 25, 2019 at 4:57 | history | edited | user3108815 | CC BY-SA 4.0 |
edited title
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| Jan 25, 2019 at 4:55 | comment | added | user3108815 | @Linas I'd like a partial sum formula for the above, ideally. | |
| Jan 24, 2019 at 18:22 | comment | added | Linas | What do you mean by "closed form"? Usually, a finite sum is considered to be a very satisfactory state of affairs; I can't quite imagine getting more "closed" than that. Anyway, have you looked at Lambert series? | |
| Jan 24, 2019 at 17:09 | comment | added | user3108815 | Would the person who downvoted me care to let me know why I've received a downvote? I would love to edit the question if I'm in violation of the (extensive) rules. | |
| Jan 24, 2019 at 7:40 | review | Close votes | |||
| Jan 27, 2019 at 18:21 | |||||
| Jan 24, 2019 at 5:31 | history | edited | user3108815 | CC BY-SA 4.0 |
edited for readability of the domain
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| Jan 24, 2019 at 5:23 | comment | added | user3108815 | edited for domain clarifications, $q$ can indeed be a rational between $0$ and $1$, or an integer $>\ 1$. | |
| Jan 24, 2019 at 5:21 | history | edited | user3108815 | CC BY-SA 4.0 |
Domain specifications
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| Jan 24, 2019 at 3:25 | review | First posts | |||
| Jan 24, 2019 at 3:29 | |||||
| Jan 24, 2019 at 3:24 | history | asked | user3108815 | CC BY-SA 4.0 |