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