Difference between revisions of "Hankel H (1)"
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(Created page with "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...") |
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$$H_{\nu}^{(1)}(z)=J_{\nu}(z)+iY_{\nu}(z),$$ | $$H_{\nu}^{(1)}(z)=J_{\nu}(z)+iY_{\nu}(z),$$ | ||
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 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]]. | ||
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| + | <gallery> | ||
| + | File:Complex hankel H1 sub 1.png|[[Domain coloring]] of [[analytic continuation]]. | ||
| + | </gallery> | ||
| + | </div> | ||
Revision as of 19:57, 19 May 2015
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.
