Unnormalized sinc function ($\mathrm{sinc}(z)={\sum }_{m\ge 0}\frac{(-1{)}^m{z}^{2m}}{(2m+1)!}$)

The sinc function $\sin z/z$ for $z\ne 0$, extended by value one at zero. The displayed power series has infinite radius of convergence, so the extension is entire. Its removable value follows from the first coefficient or from the sine limit. This convention differs by the argument scaling $z\mapsto \pi z$ from the normalized sinc convention.