Isaac Ambrose

An elliptic function integral is a function F of the form:

$x\; \backslash \; mapsto\; F\; (X)\; =\; \backslash \; int\_\; \{C\}\; ^\; \{X\}\; R\; \backslash \; bigl\; (T,\; P\; (T)\; \backslash \; bigr)\; \backslash ;\; \backslash mathrm\; dt$

where R is a rational Fonction with two variables, P is the square Racine of a polynomial function of degree 3 or 4 with simple roots and C is a constant.

The elliptic integrals “complete” of first species can be calculated by geometrical considerations.

The elliptic integrals are the applications Réciproque S of the elliptic functions.

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