Difference between revisions of "Hankel H (1)"
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The Hankel functions of the first kind are defined by | The Hankel functions of the first kind are defined by | ||
$$H_{\nu}^{(1)}(z)=J_{\nu}(z)+iY_{\nu}(z),$$ | $$H_{\nu}^{(1)}(z)=J_{\nu}(z)+iY_{\nu}(z),$$ | ||
| − | where $J_{\nu}$ is the [[Bessel J | + | 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"> | <div align="center"> | ||
Revision as of 20:10, 9 June 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.
Domain coloring of analytic continuation of $H_1^{(1)}(z)$.
Bessel functions from Abramowitz&Stegun
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Hankel $H_{\nu}^{(1)}$
