Evaluate numerically:

Evaluate to high precision:

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

Complex number inputs:

Evaluate efficiently at high precision:

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

Or compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix AngerJ function using MatrixFunction:

Limiting value at infinity:

Values at zero:

AngerJ for symbolic ν and x:

Find the first positive maximum of AngerJ:

AngerJ simplifies to BesselJ for integer orders:

Simple exact values are generated automatically:

Evaluate AngerJ for half-integer orders:

Plot the AngerJ function for integer () and half-integer () orders:

Plot the real part of :

Plot the imaginary part of :

Plot the real part of :

Plot the imaginary part of :

Real domain of :

Complex domain of :

is defined for all real values:

Complex domain is the whole plane:

Approximate function range of :

Approximate function range of :

is an even function:

is an odd function:

Use FullSimplify to simplify Anger functions:

AngerJ threads elementwise over lists:

is an analytic function of :

AngerJ is neither non-decreasing nor non-increasing:

is not injective:

is not surjective:

AngerJ is neither non-negative nor non-positive:

AngerJ does not have either singularity or discontinuity:

AngerJ is neither convex nor concave:

TraditionalForm formatting:

First derivatives with respect to z:

Higher derivatives with respect to z:

Plot the higher derivatives with respect to z when ν=1/4:

Formula for the derivative with respect to z when ν=3:

Indefinite integral of AngerJ:

More integrals:

Find the Taylor expansion using Series:

Plots of the first three approximations around :

General term in the series expansion using SeriesCoefficient:

Taylor expansion at a generic point: