Difference between revisions of "Spherical Hankel h (2)"

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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 [[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]].
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<div align="center">
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<gallery>
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File:Complex spherical hankel h2 sub 1.png|[[Domain coloring]] of [[analytic continuation]] of $h_1^{(2)}(z)$.
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</gallery>
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</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.

<center>Bessel functions
</center>