prove-that-0-1-2-m-n-

Question Number 150226 by mnjuly1970 last updated on 10/Aug/21

prove that ::

ζ (0) \overset{?}{=} \frac{- 1}{2} \dots \dots \dots .

m . n \dots

Answered by Kamel last updated on 10/Aug/21

B y u s i n g f o n c t i o n n a l r e l a t i o n o f z e t a .

Commented by mnjuly1970 last updated on 10/Aug/21

y e s m r k a m e l \dots . m e r c e y \dots

Answered by Kamel last updated on 10/Aug/21

ζ (2 n) = \frac{{(- 1)}^{n - 1} B_{2 n} {(2 π)}^{2 n}}{2 (2 n)!}, B_{n} d e n o t e B e r n o u l l i {n u m b e r}^{'} s .

∴ ζ (0) = - \frac{B_{0}}{2} = - \frac{1}{2}

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