Bernoulli formula for zeta values at nonpositive integers
= Bernoulli formula for zeta values at nonpositive integers
{c}
{title2=$\zeta(1-n)=(-1)^{n-1}B_n/n$}
For every integer $n\geq1$, the <Riemann zeta function> satisfies $\zeta(1-n)=(-1)^{n-1}B_n/n$. One proof applies <meromorphic continuation of a Mellin transform from an asymptotic expansion> to $(e^y-1)^{-1}$, whose transform is the <Bose integral> $\Gamma(s)\zeta(s)$, and divides residues by the <residues of the Gamma function>. The formula includes $\zeta(0)=-1/2$.