Latest revision as of 23:58, 22 December 2016

The Hankel functions of the second kind are defined by $$H_{\nu}^{(2)}(z)=J_{\nu}(z)-iY_{\nu}(z),$$ 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 first kind.

References

Hankel functions

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

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

Spherical Hankel $h_{\nu}^{(1)}$

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 The Hankel functions of the second kind are defined by
 $$H_{\nu}^{(2)}(z)=J_{\nu}(z)-iY_{\nu}(z),$$
-where $J_{\nu}$ is the [[Bessel J sub nu|Bessel function of the first kind]] and $Y_{\nu}$ is the [[Bessel Y sub nu|Bessel function of the second kind]]. Note the similarity of these functions to the [[Hankel H sub nu (1)|Hankel functions of the first kind]].
+where $J_{\nu}$ is the [[Bessel J|Bessel function of the first kind]] and $Y_{\nu}$ is the [[Bessel Y|Bessel function of the second kind]]. Note the similarity of these functions to the [[Hankel H (1)|Hankel functions of the first kind]].
+<div align="center">
+<gallery>
+File:Complex hankel H2 sub 1.png|[[Domain coloring]] of $H_1^{(2)}(z)$.
+</gallery>
+</div>
+=See Also=
+[[Bessel J|Bessel $J$]]<br />
+[[Bessel Y|Bessel $Y$]]<br />
+=References=
+* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Hankel H (1) in terms of csc and Bessel J|next=Hankel H (2) in terms of csc and Bessel J}}: 9.1.4
+{{:Hankel functions footer}}
+[[Category:SpecialFunction]]