generalized Bernoulli numberGeneralizedBernoulliNumber2003-01-20 16:19:272003-01-20 19:16:39Definition% this is the default PlanetMath preamble. as your knowledge
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% define commands hereLet $\chi$ be a non-trivial primitive character mod $m$. The generalized Bernoulli numbers $B_{n,\chi}$ are given by
\[
\sum_{a=1}^m \chi(a)\frac{te^{at}}{e^{mt}-1}=\sum_{n=0}^\infty B_{n,\chi}\frac{t^n}{n!}
\]
They are members of the field $\mathbb{Q}(\chi)$ generated by the values of $\chi$.