Special Functions
8.1 Elliptic Integrals and Functions
8.11 Elliptic integrals
8.110
1. Every integral of the form , where P(x) is a third- or fourth-degree polynomial, can be reduced to a linear combination of integrals leading to elementary functions and the following three integrals:
which are called respectively elliptic integrals of the first, second, and third kind in the Legendre normal form. The results of this reduction for the more frequently encountered ...
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