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 $K_{\nu}$

@@ Line 1: / Line 1: @@
 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 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">
 <gallery>
-File:Complex modified besselI sub 1.png|[[Domain coloring]] of [[analytic continuation]] of $I_1(z)$.
+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>