Skip to content

Sinc

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

Sinc[z]
    gives the cardinal sine Sin[z]/z, with Sinc[0] = 1.
An entire, even function. Sinc[+-Infinity] = 0. Real and complex inputs
evaluate numerically at machine or arbitrary (MPFR) precision;
D[Sinc[z], z] = Cos[z]/z - Sin[z]/z^2. Listable.

Examples

No verified examples yet for this function.

Implementation notes

Attributes: Listable, NumericFunction, Protected.

Implementation status

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References

Notes & additional examples

Worked examples

In[1]:= Sinc[0]
Out[1]= 1

In[1]:= Sinc[2.]
Out[1]= 0.454649

In[1]:= N[Sinc[2], 45]
Out[1]= 0.454648713412840847698009932955872421351127485

In[1]:= Sinc[1. + I]
Out[1]= 0.966711 - 0.331747 I

In[1]:= D[Sinc[x], x]
Out[1]= Cos[x]/x - Sin[x]/x^2

In[1]:= Series[Sinc[x], {x, 0, 6}]
Out[1]= 1 - x^2/6 + x^4/120 - x^6/5040 + O[x]^7

Notes

Sinc[z] is the cardinal sine Sin[z]/z, with the removable singularity at the origin filled in as Sinc[0] = 1. It is entire and even, and Sinc[±Infinity] = 0. It appears as the derivative of the sine integral: D[SinIntegral[z], z] = Sinc[z]. Numeric evaluation is at machine or arbitrary (MPFR) precision for both real and complex arguments. Listable. See also SinIntegral.