Editing Weierstrass elliptic function (section)

==Relation to Jacobi's elliptic functions==

For numerical work, it is often convenient to calculate the Weierstrass elliptic function in terms of [[Jacobi's elliptic functions]].

The basic relations are:<ref>{{cite book | author = Korn GA, [[Theresa M. Korn|Korn TM]] | year = 1961 | title = Mathematical Handbook for Scientists and Engineers | publisher = McGraw–Hill | location = New York | pages = 721 | lccn = 59014456}}</ref>
<math display="block">
\wp(z) = e_3 + \frac{e_1 - e_3}{\operatorname{sn}^2 w}
= e_2 + ( e_1 - e_3 ) \frac{\operatorname{dn}^2 w}{\operatorname{sn}^2 w}
= e_1 + ( e_1 - e_3 ) \frac{\operatorname{cn}^2 w}{\operatorname{sn}^2 w}
</math>
where <math>e_1,e_2</math> and <math>e_3</math> are the three roots described above and where the modulus ''k'' of the Jacobi functions equals
<math display="block">k = \sqrt\frac{e_2 - e_3}{e_1 - e_3}</math>
and their argument ''w'' equals
<math display="block">w = z \sqrt{e_1 - e_3}.</math>