Evaluate numerically:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Evaluate for complex numbers:

Evaluate Sinc efficiently at high precision:

Compute the elementwise values of an array using automatic threading:

Or compute the matrix Sinc function using MatrixFunction :

Compute worst-case guaranteed intervals using Interval and CenteredInterval objects:

Or compute average-case statistical intervals using Around :

Values at zero:

Values of Sinc at fixed points:

Values at infinity:

The zeros of Sinc :

Find the first positive zero using Solve :

Substitute in the result:

Visualize the result:

Plot the Sinc function:

Plot the real part of :

Plot the imaginary part of :

Polar plot with :

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:

Not surjective:

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:

TraditionalForm formatting:

First derivative:

Higher derivatives:

Indefinite integral of Sinc :

Verify the antiderivative:

Definite integral of Sinc :

More integrals:

Taylor expansion for Sinc :

Plot the first three approximations for Sinc around :

General term in the series expansion of Sinc :

The first-order Fourier series:

Sinc can be applied to a power series:

Compute the Laplace transform using LaplaceTransform :

MellinTransform :

HankelTransform :

Definition of Sinc :

Sinc of a sum:

Expand assuming real variables x and y:

Convert to exponentials:

Representation through Bessel functions:

Representation through gamma function:

Representation in terms of MeijerG :

Sinc can be represented as a DifferentialRoot :