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

Bessel functions

Anger function

Bessel $I_{\nu}$

Modified Bessel $K_{\nu}$

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 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 $i$ denotes the [[imaginary number]] and $J_{\nu}$ denotes the [[Bessel J|Bessel function of the first kind]].
+<div align="center">
+<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:Complexbesseli,n=0plot.png|[[Domain coloring]] of $I_0$.
+File:Complexbesseli,n=1plot.png|[[Domain coloring]] of $I_0$.
+File:Page 374 (Abramowitz&Stegun).jpg|Modified Bessel functions from Abramowitz&Stegun.
+</gallery>
+</div>
+=Properties=
+[[Relationship between Bessel I sub -1/2 and cosh]]<br />
+[[Relationship between Bessel I sub 1/2 and sinh]]<br />
+[[Relationship between Bessel I sub n and Bessel J sub n]]<br />
+[[Relationship between Airy Bi and modified Bessel I]]<br />
+=References=
+[[Category:SpecialFunction]]
+{{:Bessel functions footer}}