Sinc function

This article is about a particular entire function: a holomorphic function defined on the whole of

$\mathbb{C}$

View a complete list of entire functions

Definition

The sinc function is defined in the following equivalent ways:

• It is given by the power series:

$\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{c}z:=\sum _{n=0}^{\mathrm{\infty }}(-1{)}^n\frac{z^{2n}}{(2n+1)!}$

• It is defined as:

$\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{c}z:=\frac{\sin z}{z},z\ne 0,\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{c}0=1$

• It is the difference quotient of the sine function, relative to the origin.

Related functions

• Its antiderivative is the sine integral, denoted $\mathrm{S}\mathrm{i}$