Difference between revisions of "Jacobi sd"
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$$\mathrm{sd}(u)=\dfrac{\mathrm{sn}(u)}{\mathrm{dn}(u)},$$ | $$\mathrm{sd}(u)=\dfrac{\mathrm{sn}(u)}{\mathrm{dn}(u)},$$ | ||
where $\mathrm{sn}$ is the [[Jacobi sn]] function and $\mathrm{dn}$ is the [[Jacobi dn]] function. | where $\mathrm{sn}$ is the [[Jacobi sn]] function and $\mathrm{dn}$ is the [[Jacobi dn]] function. | ||
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| + | <div align="center"> | ||
| + | <gallery> | ||
| + | File:Complexjacobisd,m=0.8plot.png|[[Domain coloring]] of $\mathrm{sd}$ with $m=0.8$. | ||
| + | </gallery> | ||
| + | </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] | ||
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| + | {{:Jacobi elliptic functions footer}} | ||
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| + | [[Category:SpecialFunction]] | ||
Latest revision as of 19:08, 5 July 2016
The $\mathrm{sd}$ function is defined by $$\mathrm{sd}(u)=\dfrac{\mathrm{sn}(u)}{\mathrm{dn}(u)},$$ where $\mathrm{sn}$ is the Jacobi sn function and $\mathrm{dn}$ is the Jacobi dn function.
Domain coloring of $\mathrm{sd}$ with $m=0.8$.
References
Special functions by Leon Hall
