Summation formula

Definition

A summation formula or summation representation for a holomorphic function or meromorphic function $f:U\to \mathbb {C}$ is a holomorphic function $F$ of two variables, such that:

$f(z)=\sum _{n\in \mathbb {N} }F(z,n)$

holds on some nonempty open subset of $U$. The summation might instead be over all nonnegative integers, or over all integers, and in fact we may even have summations over all the Gaussian integers instead.

Related notions

• Integral formula