Legendre Form

$F(\backslash phi,k)\; =\; \backslash int\_0^\backslash phi\; \backslash frac\{1\}\{\backslash sqrt\{1\; -\; k^2\; \backslash sin^2(t)\}\}\; dt,$

$E(\backslash phi,k)\; =\; \backslash int\_0^\backslash phi\; \backslash sqrt\{1\; -\; k^2\; \backslash sin^2(t)\}\backslash ,dt,$

$P(\backslash phi,k,n)\; =\; \backslash int\_0^\backslash phi\; \backslash frac\{1\}\{(1\; +\; n\; \backslash sin^2(t))\backslash sqrt\{1\; -\; k^2\; \backslash sin^2(t)\}\}\backslash ,dt.$

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