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riemann_zeta_function [2015/12/27 17:23] nikolaj |
riemann_zeta_function [2016/05/31 20:20] nikolaj |
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| ^ $\zeta(-2m)=0$ ^ | ^ $\zeta(-2m)=0$ ^ | ||
| ^ $\zeta(2m)=(-1)^{m+1}\frac{(2\pi)^{2m}}{2(2m)!} B_{2m}$ ^ | ^ $\zeta(2m)=(-1)^{m+1}\frac{(2\pi)^{2m}}{2(2m)!} B_{2m}$ ^ | ||
| + | |||
| + | so that | ||
| + | |||
| + | $\zeta(1-2m)=(-1)^{m+1}\frac{1}{2m}B_{2m}$ | ||
| + | |||
| E.g. | E.g. | ||
| ^ $\zeta(2)=\pi^2/6$ ^ | ^ $\zeta(2)=\pi^2/6$ ^ | ||
