Legendre Elliptic Integral Second Kind phi sin(alpha) actual elle(phi,ak) 0.09 0.03 8.726633e-02 8.726633e-02 0.09 0.50 8.723881e-02 8.723880e-02 0.09 1.00 8.715588e-02 8.715588e-02 0.52 0.03 5.235712e-01 5.235712e-01 0.52 0.50 5.178819e-01 5.178820e-01 0.52 1.00 5.000300e-01 5.000300e-01 1.57 0.03 1.570318e+00 1.570318e+00 1.57 0.50 1.467462e+00 1.467462e+00 1.57 1.00 1.002584e+00 1.002584e+00