The incomplete elliptic integral of the second kind E in trigonometric form is
Substituting, one obtains Jacobi's form:
Equivalently, in terms of the amplitude and modular angle:
Relations with the Jacobi elliptic functions include
The meridian arc length from the equator to latitude is written in terms of E:
where a is the semi-major axis, and e is the eccentricity.
Read more about this topic: Elliptic Integral
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