Legendre Elliptic Integral Third Kind phi -en sin(alpha) actual ellpi(phi,ak) 0.26 -0.40 0.50 2.649530e-01 2.649535e-01 1.05 -0.60 1.00 1.719510e+00 1.719512e+00 1.57 0.00 0.50 1.685750e+00 1.685750e+00 1.57 -0.90 0.97 1.246407e+01 1.246409e+01 0.26 -1.00 0.26 2.681560e-01 2.681556e-01 0.79 -0.06 0.50 8.138450e-01 8.138455e-01 0.79 -0.62 0.50 9.211300e-01 9.211296e-01 0.79 -1.25 0.50 1.132136e+00 1.132136e+00 0.79 0.25 0.50 7.698720e-01 7.698724e-01 1.57 -0.06 0.50 1.743055e+00 1.743055e+00 1.57 -0.62 0.50 2.800989e+00 2.800989e+00 1.57 0.25 0.50 1.501762e+00 1.501762e+00