BesselI
BesselI[n,z]
gives the modified Bessel function of the first kind .
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
satisfies the differential equation
.
- BesselI[n,z] has a branch cut discontinuity in the complex z plane running from
to
.
- FullSimplify and FunctionExpand include transformation rules for BesselI.
- For certain special arguments, BesselI automatically evaluates to exact values.
- BesselI can be evaluated to arbitrary numerical precision.
- BesselI 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 (42)
Numerical Evaluation (5)
Specific Values (4)
Visualization (4)
Function Properties (5)
is defined for all real and complex values:
is defined and real for all real values greater than 0:
Complex domain is the whole plane except :
achieves all real values greater than 1:
achieves all real positive values:
For integer ,
is an even or odd function in
depending on whether
is even or odd:
TraditionalForm formatting:
Differentiation (3)
Integration (4)
Series Expansions (6)
Integral Transforms (3)
Function Identities and Simplifications (3)
Applications (1)
Properties & Relations (4)
Use FullSimplify to simplify expressions with BesselI:
Find limits of expressions involving BesselI:
Series representation of BesselI:
The exponential generating function for BesselI:
Possible Issues (1)
Text
Wolfram Research (1988), BesselI, Wolfram Language function, https://reference.wolfram.com/language/ref/BesselI.html (updated 2002).
BibTeX
BibLaTeX
CMS
Wolfram Language. 1988. "BesselI." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2002. https://reference.wolfram.com/language/ref/BesselI.html.
APA
Wolfram Language. (1988). BesselI. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BesselI.html