Editing Jacobi elliptic functions (section)

=== Relations between squares of the functions ===
Relations between squares of the functions can be derived from two basic relationships (Arguments (''u'',''m'') suppressed):
<math display="block">\operatorname{cn}^2+\operatorname{sn}^2=1</math>
<math display="block">\operatorname{cn}^2+m' \operatorname{sn}^2=\operatorname{dn}^2</math>
where ''m&nbsp;+&nbsp;m'&nbsp;''=&nbsp;1. Multiplying by any function of the form ''nq'' yields more general equations:

<math display="block">\operatorname{cq}^2+\operatorname{sq}^2=\operatorname{nq}^2</math>
<math display="block">\operatorname{cq}^2{}+m' \operatorname{sq}^2=\operatorname{dq}^2</math>

With ''q''&nbsp;=&nbsp;''d'', these correspond trigonometrically to the equations for the unit circle (<math>x^2+y^2=r^2</math>) and the unit ellipse  (<math>x^2{}+m' y^2=1</math>), with ''x''&nbsp;=&nbsp;''cd'', ''y''&nbsp;=&nbsp;''sd'' and ''r''&nbsp;=&nbsp;''nd''. Using the multiplication rule, other relationships may be derived. For example:

<math display="block">
-\operatorname{dn}^2{}+m'= -m\operatorname{cn}^2 = m\operatorname{sn}^2-m
</math>

<math display="block">
-m'\operatorname{nd}^2{}+m'= -mm'\operatorname{sd}^2 = m\operatorname{cd}^2-m
</math>

<math display="block">
m'\operatorname{sc}^2{}+m'= m'\operatorname{nc}^2 = \operatorname{dc}^2-m
</math>

<math display="block">
\operatorname{cs}^2{}+m'=\operatorname{ds}^2=\operatorname{ns}^2-m
</math>