Latest revision as of 23:59, 22 December 2016

The Hankel functions of the first kind are defined by $$H_{\nu}^{(1)}(z)=J_{\nu}(z)+iY_{\nu}(z),$$ where $J_{\nu}$ is the Bessel function of the first kind and $Y_{\nu}$ is the Bessel function of the second kind. Note the similarity of these functions to the Hankel functions of the second kind.

References

Hankel functions

Hankel $H_{\nu}^{(1)}$

Hankel $H_{\nu}^{(2)}$

@@ Line 5: / Line 5: @@
 <div align="center">
 <gallery>
-File:Complex hankel H1 sub 1.png|[[Domain coloring]] of [[analytic continuation]] of $H_1^{(1)}(z)$.
+File:Complex hankel H1 sub 1.png|[[Domain coloring]] of $H_1^{(1)}(z)$.
 File:Page 359Abramowitz-Stegun(Bessel functions).jpg|Bessel functions from [http://dualaud.net/specialfunctionswiki/abramowitz_and_stegun-1.03/ Abramowitz&Stegun]
 </gallery>