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Particular values of Riemann zeta function
・ Particular values of the Gamma function
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Particular values of Riemann zeta function : ウィキペディア英語版
Particular values of Riemann zeta function
This article gives some specific values of the Riemann zeta function, including values at integer arguments, and some series involving them.
==The Riemann zeta function at 0 and 1==
At zero, one has
:\zeta(0)= -B_1=-\tfrac.\!
At 1 there is a pole, so ζ(1) is not defined but the left and right limits are:
:\lim_{\epsilon\to 0^{\pm}}\zeta(1+\epsilon) = \pm\infty.
Since it is a pole of first order, its principal value exists and is equal to the Euler–Mascheroni constant γ = 0.57721 56649+.

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