Difference between revisions of "Modified Bessel I"

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The modified Bessel function of the first kind is defined by
 
The modified Bessel function of the first kind is defined by
 
$$I_{\nu}(z)=i^{-\nu}J_{\nu}(iz),$$
 
$$I_{\nu}(z)=i^{-\nu}J_{\nu}(iz),$$
where $J_{\nu}$ is the [[Bessel J|Bessel function of the first kind]].
+
where $i$ denotes the [[imaginary number]] and $J_{\nu}$ denotes the [[Bessel J|Bessel function of the first kind]].
  
 
<div align="center">
 
<div align="center">
 
<gallery>
 
<gallery>
 +
File:Besseli,n=0plot.png|Graph of $I_0$.
 +
File:Besseli,n=1plot.png|Graph of $I_1$.
 
File:Multiplebesseliplot.png|Graph of $I_0$,$I_1$,$I_2$, and $I_3$.
 
File:Multiplebesseliplot.png|Graph of $I_0$,$I_1$,$I_2$, and $I_3$.
 
File:Complexbesseli,n=0plot.png|[[Domain coloring]] of $I_0$.
 
File:Complexbesseli,n=0plot.png|[[Domain coloring]] of $I_0$.

Latest revision as of 23:53, 10 June 2016

The modified Bessel function of the first kind is defined by $$I_{\nu}(z)=i^{-\nu}J_{\nu}(iz),$$ where $i$ denotes the imaginary number and $J_{\nu}$ denotes the Bessel function of the first kind.

Properties

Relationship between Bessel I sub -1/2 and cosh
Relationship between Bessel I sub 1/2 and sinh
Relationship between Bessel I sub n and Bessel J sub n
Relationship between Airy Bi and modified Bessel I

References

Bessel functions