Difference between revisions of "Modified Bessel I"

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File:Complex modified besselI sub 1.png|[[Domain coloring]] of [[analytic continuation]] of $I_1(z)$.
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File:Complexbesseli,n=0plot.png|[[Domain coloring]] of $I_0$.
 
File:Page 374 (Abramowitz&Stegun).jpg|Modified Bessel functions from Abramowitz&Stegun.
 
File:Page 374 (Abramowitz&Stegun).jpg|Modified Bessel functions from Abramowitz&Stegun.
 
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Revision as of 23:23, 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.

  • Domain coloring of $I_0$.

  • Modified Bessel functions from Abramowitz&Stegun.

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

Anger function

Bessel-Clifford

Bessel $J_{\nu}$

Bessel $Y_{\nu}$

Bessel $I_{\nu}$

Modified Bessel $K_{\nu}$

Spherical Bessel $j_{\nu}$

Spherical Bessel $y_{\nu}$
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