Difference between revisions of "Modified Bessel I"

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File:Multiplebesseliplot.png|Graph of $I_0$.
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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 $I_0$.
 
File:Complexbesseli,n=1plot.png|[[Domain coloring]] of $I_0$.
 
File:Complexbesseli,n=1plot.png|[[Domain coloring]] of $I_0$.

Revision as of 23:34, 10 June 2016

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