gives the Bessel function of the first kind .
- Mathematical function, suitable for both symbolic and numerical manipulation.
- satisfies the differential equation .
- BesselJ[n,z] has a branch cut discontinuity in the complex z plane running from to .
- FullSimplify and FunctionExpand include transformation rules for BesselJ.
- For certain special arguments, BesselJ automatically evaluates to exact values.
- BesselJ can be evaluated to arbitrary numerical precision.
- BesselJ automatically threads over lists.
- BesselJ can be used with Interval and CenteredInterval objects. »
Examplesopen allclose all
Basic Examples (5)
Series expansion at Infinity:
Numerical Evaluation (6)
Evaluate BesselJ efficiently at high precision:
Specific Values (3)
Function Properties (12)
BesselJ is neither non-decreasing nor non-increasing:
BesselJ is not injective:
BesselJ is not surjective:
BesselJ is neither non-negative nor non-positive:
BesselJ is neither convex nor concave:
Indefinite integral of an expression involving BesselJ:
Series Expansions (6)
General term in the series expansion of BesselJ:
Asymptotic approximation of BesselJ:
BesselJ can be applied to a power series:
Integral Transforms (4)
Function Identities and Simplifications (4)
Use FullSimplify to simplify Bessel functions:
Fraunhofer diffraction is the type of diffraction that occurs in the limit of a small Fresnel number. Plot the intensity of the Fraunhofer diffraction pattern of a circular aperture versus diffraction angle:
Properties & Relations (5)
Wolfram Research (1988), BesselJ, Wolfram Language function, https://reference.wolfram.com/language/ref/BesselJ.html (updated 2022).
Wolfram Language. 1988. "BesselJ." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/BesselJ.html.
Wolfram Language. (1988). BesselJ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BesselJ.html