AngerJ
Details
![](Files/AngerJ.en/details_1.png)
- Mathematical function, suitable for both symbolic and numerical manipulation.
satisfies the differential equation
.
is defined by
.
- AngerJ[ν,z] is an entire function of z with no branch cut discontinuities.
is defined by
.
- For certain special arguments, AngerJ automatically evaluates to exact values.
- AngerJ can be evaluated to arbitrary numerical precision.
- AngerJ automatically threads over lists.
- AngerJ can be used with Interval and CenteredInterval objects. »
Examples
open allclose allBasic Examples (4)
Scope (39)
Numerical Evaluation (6)
The precision of the output tracks the precision of the input:
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:
Specific Values (7)
Visualization (3)
Plot the AngerJ function for integer () and half-integer (
) orders:
Function Properties (15)
is defined for all real values:
Complex domain is the whole plane:
Approximate function range of :
Approximate function range of :
Use FullSimplify to simplify Anger functions:
AngerJ threads elementwise over lists:
AngerJ is neither non-decreasing nor non-increasing:
AngerJ is neither non-negative nor non-positive:
AngerJ does not have either singularity or discontinuity:
AngerJ is neither convex nor concave:
TraditionalForm formatting:
Differentiation and Integration (5)
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:
Series Expansions (3)
Find the Taylor expansion using Series:
Plots of the first three approximations around :
General term in the series expansion using SeriesCoefficient:
Properties & Relations (2)
Use FunctionExpand to expand AngerJ into hypergeometric functions:
Text
Wolfram Research (2008), AngerJ, Wolfram Language function, https://reference.wolfram.com/language/ref/AngerJ.html.
CMS
Wolfram Language. 2008. "AngerJ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AngerJ.html.
APA
Wolfram Language. (2008). AngerJ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AngerJ.html