Timeline for What is the $q$-analog of $\Gamma(z)\Gamma(1-z)=\frac\pi{\sin(\pi z)}$?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jan 21, 2020 at 17:26 | comment | added | მამუკა ჯიბლაძე | @TheWheelisBeforeDescartes The q-deformed Gamma function and q-deformed polygamma function by Won Sang Chung, Taekyun Kim, and Toufik Mansour (Bull. Korean Math. Soc. 51 (2014), no. 4, 1155-1161) | |
| Jan 21, 2020 at 15:46 | comment | added | Descartes Before the Horse | @MartinBokner Hi, I can't access that file - any chance you have another working link? | |
| Aug 26, 2017 at 7:14 | comment | added | მამუკა ჯიბლაძე | @MartinBokner Astounding paper indeed, thank you very much for the reference! | |
| Aug 25, 2017 at 23:16 | comment | added | Martin Bokner | Also, the following article discusses $q$-analogues of the Euler reflection formula. icms.kaist.ac.kr/mathnet/thesis_file/BKMS-51-4-1155-1161.pdf | |
| Aug 16, 2015 at 21:16 | comment | added | მამუკა ჯიბლაძე | @DietrichBurde After some confusion, I've checked the paper and it seems that they get the same which made me stuck: denoting $\Gamma_q(x)\Gamma_q(1-x)=f(q^x)$, one obtains$$f(qz)=-zf(z),$$whereas I would expect to obtain a function with $f(qz)=f(z)$. | |
| Aug 15, 2015 at 21:51 | comment | added | Terry Tao | This is a very different use of the letter "q", but the "q-aspect" version of the identity $\Gamma(z) \Gamma(1-z) = \frac{\pi}{\sin \pi z}$ in analytic number theory is the identity $\tau(\chi) \tau(\overline{\chi}) = q \chi(-1)$ for Gauss sums $\tau(\chi) = \sum_{n \in {\bf Z}/q{\bf Z}} \chi(n) e(n/q)$ of Dirichlet characters of conductor $q$. (Gauss sums show up in the functional equation for Dirichlet L-functions in much the same way that Gamma factors show up for the Riemann zeta function.) | |
| Aug 15, 2015 at 21:30 | comment | added | მამუკა ჯიბლაძე | @DietrichBurde Thanks a lot, I would never find it myself! Would you make it an answer? | |
| Aug 15, 2015 at 18:46 | comment | added | Dietrich Burde | This article discusses $q$-analogues of the Euler reflection formula and the Euler gamma integral. | |
| Aug 15, 2015 at 18:10 | history | asked | მამუკა ჯიბლაძე | CC BY-SA 3.0 |