Difference between revisions of "Hankel H (2)"
From specialfunctionswiki
(Created page with "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]...") |
|||
| Line 2: | Line 2: | ||
$$H_{\nu}^{(2)}(z)=J_{\nu}(z)-iY_{\nu}(z),$$ | $$H_{\nu}^{(2)}(z)=J_{\nu}(z)-iY_{\nu}(z),$$ | ||
where $J_{\nu}$ is the [[Bessel J 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 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]]. | ||
| + | |||
| + | <div align="center"> | ||
| + | <gallery> | ||
| + | File:Complex hankel H2 sub 1.png|[[Domain coloring]] of [[analytic continuation]] of $H_1^{(2)}(z)$. | ||
| + | </gallery> | ||
| + | </div> | ||
Revision as of 20:00, 19 May 2015
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.
Domain coloring of analytic continuation of $H_1^{(2)}(z)$.
