Definition:Elliptic Integral of the First Kind/Incomplete

Definition 2
Note that:
 * $\map F {k, \dfrac \pi 2} = \map K k$

where $\map K k$ denotes the complete elliptic integral of the first kind.

Also known as
Some sources omit the incomplete from the definition, calling this merely the elliptic integral of the first kind.

Also see

 * Equivalence of Definitions of Incomplete Elliptic Integral of the First Kind


 * Definition:Complete Elliptic Integral of the First Kind


 * Definition:Elliptic Integral of the Second Kind:
 * Definition:Incomplete Elliptic Integral of the Second Kind
 * Definition:Complete Elliptic Integral of the Second Kind


 * Definition:Elliptic Integral of the Third Kind:
 * Definition:Incomplete Elliptic Integral of the Third Kind
 * Definition:Complete Elliptic Integral of the Third Kind