BesselK
BesselK[n,z]
gives the modified Bessel function of the second kind .
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
satisfies the differential equation
.
- BesselK[n,z] has a branch cut discontinuity in the complex z plane running from
to
.
- FullSimplify and FunctionExpand include transformation rules for BesselK.
- For certain special arguments, BesselK automatically evaluates to exact values.
- BesselK can be evaluated to arbitrary numerical precision.
- BesselK automatically threads over lists.
Examples
open allclose allBasic Examples (5)
Plot over a subset of the reals:
Plot over a subset of the complexes:
Series expansion at the origin:
Series expansion at Infinity:
Scope (37)
Numerical Evaluation (5)
Specific Values (4)
Visualization (3)
Function Properties (4)
is defined for all real values greater than 0:
For real ,
achieves all positive real values:
BesselK is an even function with respect to the first parameter:
TraditionalForm formatting:
Differentiation (3)
Integration (3)
Series Expansions (5)
Integral Transforms (3)
Function Identities and Simplifications (3)
Applications (1)
Properties & Relations (2)
Text
Wolfram Research (1988), BesselK, Wolfram Language function, https://reference.wolfram.com/language/ref/BesselK.html (updated 2002).
BibTeX
BibLaTeX
CMS
Wolfram Language. 1988. "BesselK." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2002. https://reference.wolfram.com/language/ref/BesselK.html.
APA
Wolfram Language. (1988). BesselK. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BesselK.html