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

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 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 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 (2)|Hankel functions of the second kind]].
+where $J_{\nu}$ is the [[Bessel J|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 (2)|Hankel functions of the second kind]].
 <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>
 </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=Bessel Y|next=Hankel H (1) in terms of csc and Bessel J}}: 9.1.3
+{{:Hankel functions footer}}
+[[Category:SpecialFunction]]