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elli3() double elli3 ( double  phi, double  n, double  k  ) Incomplete elliptic integral of the third kind P(phi, n, k) Purpose elli3 computes the Legendre form of incomplete elliptic integral of the third kind P(φ, n, k). P(φ, n, k) = ∫ 1/((1 - n(sin(t))^2)sqrt(1 - k^2(sin(t))^2)) dt [0, φ] Returns Incomplete elliptic integral of the third kind P(φ, n, k). Parameters [in] phi Argument φ [rad]. [in] n Argument n. (n < 1/sin(phi)^2 (if |phi| > π/2, n < 1)) [in] k Argument k. (k^2*sin(phi)^2 < 1 (if |phi| > π/2, |k| < 1)) Error handling If n >= 1/sin(phi)^2), domain error (EDOM) occurs. If k^2*sin(phi)^2 >= 1 (|k| >= 1 if |phi| > π/2), domain error (EDOM) occurs. Range error (ERANGE) may occur. Reference boost/math/special_functions