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