Timeline for Complex proof of $B(a,b)=\Gamma(a)\Gamma(b)/\Gamma(a+b)$
Current License: CC BY-SA 3.0
16 events
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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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| Feb 6, 2016 at 16:24 | comment | added | Sergei | We may take an integral using a technique based on Slater's Theorem (cf. O.I.Marichev's book). In fact it will use in an inderect way contour integrals and residues. | |
| S Jan 30, 2016 at 8:50 | history | suggested | Ali Taghavi |
I add a tag
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| Jan 30, 2016 at 8:37 | review | Suggested edits | |||
| S Jan 30, 2016 at 8:50 | |||||
| Jan 20, 2016 at 18:53 | comment | added | Fedor Petrov | @TomCopeland say, parallelogram here is perfect: mathoverflow.net/questions/105457/… | |
| Jan 20, 2016 at 18:41 | comment | added | Tom Copeland | Real integrals such as those for the gamma function and Riemann zeta (standard Mellin transforms for Re(s) > 0) can be expanded to complex integrals using the Hankel contour, just as Riemann did in his famous paper on the Reimann zeta. The same can be done for the beta integral, which is a particularly simple Mellin transform at the foundations of one class of fractional calculus that has been developed any number of ways and for which Euler developed his iconic integral for the gamma function. Which contour integral are you really looking for? | |
| Jan 16, 2016 at 22:35 | answer | added | Loïc Teyssier | timeline score: 3 | |
| Jan 16, 2016 at 20:59 | comment | added | Pietro Majer | ok; $ \int u*v=(\int u)(\int v)$ is indeed Fubini | |
| Jan 16, 2016 at 19:27 | comment | added | Fedor Petrov | @Pietro it is probably most common proof, what I call "Fubini". | |
| Jan 16, 2016 at 19:23 | history | edited | Fedor Petrov | CC BY-SA 3.0 |
edited body
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| Jan 16, 2016 at 18:22 | comment | added | Pietro Majer | The way I like to of see that identity is, seeing it as a consequence of the fact that the integral of a convolution is the product of integrals, as mentioned here mathoverflow.net/questions/20960/…. | |
| Jan 16, 2016 at 17:32 | answer | added | Kostya_I | timeline score: 1 | |
| Jan 16, 2016 at 14:45 | answer | added | Sergei | timeline score: 0 | |
| Jan 16, 2016 at 14:09 | comment | added | Fedor Petrov | Pochhammer formula relates integral over $[0,1]$ and integral over Pochhammer contour, but how does it express any of above integrals via $\Gamma$-function? | |
| Jan 16, 2016 at 14:03 | comment | added | Loïc Teyssier | Isn't what Pochhammer formula is about? | |
| Jan 16, 2016 at 9:41 | history | asked | Fedor Petrov | CC BY-SA 3.0 |