Difference between revisions of "Jacobi ds"

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$$\mathrm{ds}(u)=\dfrac{\mathrm{dn}(u)}{\mathrm{sn}(u)},$$
 
$$\mathrm{ds}(u)=\dfrac{\mathrm{dn}(u)}{\mathrm{sn}(u)},$$
 
where $\mathrm{dn}$ is the [[Jacobi dn]] function and $\mathrm{sn}$ is the [[Jacobi sn]] function.
 
where $\mathrm{dn}$ is the [[Jacobi dn]] function and $\mathrm{sn}$ is the [[Jacobi sn]] function.
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<div align="center">
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<gallery>
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File:Complexjacobids,m=0.8plot.png|[[Domain coloring]] of $\mathrm{ds}$ corresponding to $m=0.8$.
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</gallery>
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</div>
  
 
=References=
 
=References=
 
[http://web.mst.edu/~lmhall/SPFNS/spfns.pdf Special functions by Leon Hall]
 
[http://web.mst.edu/~lmhall/SPFNS/spfns.pdf Special functions by Leon Hall]
  
<center>{{:Jacobi elliptic functions footer}}</center>
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{{:Jacobi elliptic functions footer}}
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[[Category:SpecialFunction]]

Latest revision as of 19:07, 5 July 2016

The $\mathrm{ds}$ function is defined by $$\mathrm{ds}(u)=\dfrac{\mathrm{dn}(u)}{\mathrm{sn}(u)},$$ where $\mathrm{dn}$ is the Jacobi dn function and $\mathrm{sn}$ is the Jacobi sn function.

References

Special functions by Leon Hall

Jacobi Elliptic Functions