The incomplete elliptic integral of the third kind Π is
, or
The number n is called the characteristic and can take on any value, independently of the other arguments. Note though that the value is infinite, for any m.
A relation with the Jacobian elliptic functions is
The meridian arc length from the equator to latitude is also related to a special case of Π:
Read more about this topic: Elliptic Integral
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