Difference between revisions of "Spherical Hankel h (2)"
From specialfunctionswiki
| Line 2: | Line 2: | ||
$$h_{\nu}^{(1)}(z)=j_{\nu}(z)-iy_{\nu}(z),$$ | $$h_{\nu}^{(1)}(z)=j_{\nu}(z)-iy_{\nu}(z),$$ | ||
where $j_{\nu}$ is the [[Spherical Bessel j sub nu|spherical Bessel function of the first kind]] and $y_{\nu}$ is the [[Spherical Bessel y sub nu|spherical Bessel function of the second kind]]. | where $j_{\nu}$ is the [[Spherical Bessel j sub nu|spherical Bessel function of the first kind]] and $y_{\nu}$ is the [[Spherical Bessel y sub nu|spherical Bessel function of the second kind]]. | ||
| + | |||
| + | <div align="center"> | ||
| + | <gallery> | ||
| + | File:Complex spherical hankel h2 sub 1.png|[[Domain coloring]] of [[analytic continuation]] of $h_1^{(2)}(z)$. | ||
| + | </gallery> | ||
| + | </div> | ||
<center>{{:Bessel functions footer}}</center> | <center>{{:Bessel functions footer}}</center> | ||
Revision as of 20:33, 19 May 2015
The spherical Hankel function $h_{\nu}^{(2)}$ is defined by $$h_{\nu}^{(1)}(z)=j_{\nu}(z)-iy_{\nu}(z),$$ where $j_{\nu}$ is the spherical Bessel function of the first kind and $y_{\nu}$ is the spherical Bessel function of the second kind.
Domain coloring of analytic continuation of $h_1^{(2)}(z)$.
