- Mathematical function, suitable for both symbolic and numerical manipulation.
- The argument of Sinc is assumed to be in radians. (Multiply by Degree to convert from degrees.)
- Sinc[z] is equivalent to Sin[z]/z for , but is 1 for .
- For certain special arguments, Sinc automatically evaluates to exact values.
- Sinc can be evaluated to arbitrary numerical precision.
- Sinc can be used with Interval and CenteredInterval objects. »
- Sinc automatically threads over lists.
Examplesopen allclose all
Basic Examples (4)
The argument is given in radians:
Plot over a subset of the complexes:
Find the Fourier transform of Sinc:
Numerical Evaluation (6)
The precision of the output tracks the precision of the input:
Evaluate Sinc efficiently at high precision:
Sinc threads elementwise over lists and matrices:
Sinc can be used with Interval and CenteredInterval objects:
Specific Values (4)
Plot the Sinc function:
Function Properties (10)
Sinc is defined for all real and complex values:
Approximate real range of Sinc:
Sinc is an even function:
Sinc is an analytic function of x:
Sinc is monotonic in a specific range:
Sinc is not injective:
Sinc is neither non-negative nor non-positive:
Sinc has no singularities or discontinuities:
Sinc is neither convex nor concave:
In [-π/2, π/2], it is concave:
Series Expansions (4)
Integral Transforms (3)
Compute the Laplace transform using LaplaceTransform:
Function Identities and Simplifications (4)
Function Representations (4)
Representation through Bessel functions:
Representation through gamma function:
Representation in terms of MeijerG:
Sinc can be represented as a DifferentialRoot:
Properties & Relations (2)
Use FunctionExpand to expand expressions involving Sinc:
Use FullSimplify to simplify expressions involving Sinc:
Possible Issues (1)
Non‐trivial minima and maxima of Sinc do not have ordinary closed forms:
Wolfram Research (2007), Sinc, Wolfram Language function, https://reference.wolfram.com/language/ref/Sinc.html (updated 2021).
Wolfram Language. 2007. "Sinc." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/Sinc.html.
Wolfram Language. (2007). Sinc. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Sinc.html