Timeline for Why does the Gamma-function complete the Riemann Zeta function?
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4 events
| when toggle format | what | by | license | comment | |
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| Jan 5, 2017 at 21:21 | comment | added | Tom Copeland | See also math.stackexchange.com/questions/143449/… | |
| Nov 11, 2015 at 22:01 | comment | added | M Mueger | Actually, not quite. Define $\eta(z)=(1-2^{1-z})\zeta(z)=\sum_{n\ge 1}\frac{(-1)^{n+1}}{n^z}$. This sum converges (conditionally) when Re$\,z>0$, thus $\eta$ is defined in the same half-plane (modulo considerations for Re$\,z=1$. The functional equation for $\zeta$ leads to a functional equation for $\eta$. The latter makes sense without complex analysis since $\eta(s)$ and $\eta(1-s)$ are both defined if $0<s<1$. This functional equation was already published by Euler! See: 1) E. Landau: Euler und die Funktionalgleichung der Riemannschen Zetafunktion. 2) A. Weil: Prehistory of the zeta-func. | |
| May 19, 2012 at 15:33 | comment | added | Tom Copeland | Related to mathoverflow.net/questions/58004/…. | |
| Dec 3, 2009 at 22:11 | history | answered | Ricardo | CC BY-SA 2.5 |