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:

$\operatorname {sinc} z:=\sum _{n=0}^{\infty }(-1)^{n}{\frac {z^{2n}}{(2n+1)!}}$

• It is defined as:

$\operatorname {sinc} z:={\frac {\sin z}{z}},\ z\neq 0,\qquad \operatorname {sinc} 0=1$

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

Related functions

• Its antiderivative is the sine integral, denoted $\operatorname {Si}$