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 $J_{\nu}$ | + | 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.
Graph of $I_0$.
Graph of $I_1$.
Graph of $I_0$,$I_1$,$I_2$, and $I_3$.
Domain coloring of $I_0$.
Domain coloring of $I_0$.
Modified Bessel functions from Abramowitz&Stegun.
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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
