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Elliptic integral of the first kind ( $F (z, k)$ )

For a parameter

k

, one form of the incomplete elliptic integral of the first kind is

F (z, k) = \int_{0}^{z} \frac{d t}{( 1 - t ^{2} ) ( 1 - k ^{2} t ^{2} )} .

Its value depends on the choices of square-root branches and, under analytic continuation around the branch points, on the integration path.

Table of contents 57 2
- Complete elliptic integral of the first kind Elliptic integral of the first kind 21 1
  - Complementary complete elliptic integral of the first kind Complete elliptic integral of the first kind 8

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