Timeline for Relation between two hypergeometric series
Current License: CC BY-SA 2.5
16 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Nov 14, 2010 at 21:19 | history | edited | Blue | CC BY-SA 2.5 |
added reference to another MathOverflow post for context
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| Nov 14, 2010 at 12:10 | comment | added | J. M. isn't a mathematician | After days of playing around, I have to agree that it's very tantalizing; I suspect some weird identity for the Lerch transcendent may be the key (since Dirichlet series and the polylogarithms are special cases of the Lerch transcendent). | |
| Nov 12, 2010 at 20:14 | comment | added | Suvrit | Yes, I also played around; first you have $16^k$; if you had $(-16)^k$ then things would simplify dramatically I think. | |
| Nov 10, 2010 at 20:43 | comment | added | Blue | @Suvrit: Interestingly, Adamchik uses that trick in Entry 30 here cs.cmu.edu/~adamchik/articles/catalan/catalan.htm to get a series for Catalan's constant that's almost like the series for $T(1/2)$, except my $16^k$ is his $8^k$. (So close!) Applying the trick to the $T(1/2)$ series gives an integral that Mathematica immediately evaluates to what is effectively the dilogarithm formula. | |
| Nov 9, 2010 at 22:27 | comment | added | Suvrit | does the standard trick of writing $1/(2k+1) = \int_0^1 x^{2k}dx$ help? | |
| Nov 9, 2010 at 20:26 | history | edited | Blue | CC BY-SA 2.5 |
added dilogarithm rep of T(1/2) and hypergeom rep of G
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| Nov 9, 2010 at 15:49 | comment | added | J. M. isn't a mathematician | Another integral representation: $2\int_0^{\pi/6}u\cot\;u\mathrm{d}u$ | |
| Nov 9, 2010 at 15:20 | comment | added | J. M. isn't a mathematician | From functions.wolfram.com/HypergeometricFunctions/Hypergeometric3F2/… , we get an integral representation for $T(1/2)$: $\int_0^1 \frac1{u}\arcsin\left(\frac{\sqrt{u}}{2}\right)\mathrm{d}u$. | |
| Nov 9, 2010 at 15:13 | comment | added | J. M. isn't a mathematician | $T(1/2)$ is expressible in terms of dilogarithms: functions.wolfram.com/HypergeometricFunctions/Hypergeometric3F2/… | |
| Nov 9, 2010 at 10:33 | history | edited | Blue | CC BY-SA 2.5 |
added focus on r=1/2 and catalan constant
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| Nov 9, 2010 at 10:10 | history | edited | Blue | CC BY-SA 2.5 |
fixed embarrassing typo in title
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| Nov 9, 2010 at 10:02 | comment | added | Blue | @J. M.: Checking them now ... :) | |
| Nov 9, 2010 at 10:00 | history | edited | Blue | CC BY-SA 2.5 |
added "3F2" representations
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| Nov 9, 2010 at 9:38 | comment | added | J. M. isn't a mathematician | Mathematica says they're both ${}_3 F_2$ functions. I'll take a look, but in the meantime, have you checked dlmf.nist.gov/16 and functions.wolfram.com/HypergeometricFunctions/Hypergeometric3F2 ? | |
| Nov 9, 2010 at 9:30 | history | asked | Blue | CC BY-SA 2.5 |