Difference between revisions of "Hankel H (2)"

From specialfunctionswiki
Jump to: navigation, search
 
(2 intermediate revisions by the same user not shown)
Line 1: Line 1:
 
The Hankel functions of the second kind are defined by
 
The Hankel functions of the second kind are defined by
 
$$H_{\nu}^{(2)}(z)=J_{\nu}(z)-iY_{\nu}(z),$$
 
$$H_{\nu}^{(2)}(z)=J_{\nu}(z)-iY_{\nu}(z),$$
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 (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">
 
<div align="center">
 
<gallery>
 
<gallery>
File:Complex hankel H2 sub 1.png|[[Domain coloring]] of [[analytic continuation]] of $H_1^{(2)}(z)$.
+
File:Complex hankel H2 sub 1.png|[[Domain coloring]] of $H_1^{(2)}(z)$.
 
</gallery>
 
</gallery>
 
</div>
 
</div>
Line 13: Line 13:
 
[[Bessel Y|Bessel $Y$]]<br />
 
[[Bessel Y|Bessel $Y$]]<br />
  
<center>{{:Hankel functions footer}}</center>
+
=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]]
 
[[Category:SpecialFunction]]

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.

See Also

Bessel $J$
Bessel $Y$

References

Hankel functions