Legendre form

Encyclopedia : L : LE : LEG : Legendre form

In mathematics, the Legendre forms of elliptic integrals, F(φ,k), E(φ,k) and P(φ,k,n) are defined by

[F(\phi,k) = \int_0^\phi \frac} dt,]

[E(\phi,k) = \int_0^\phi \sqrt\,dt,]

and

[P(\phi,k,n) = \int_0^\phi \frac}\,dt.]

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