Legendre Polynomials

   n    m          x            actual            plgndr(n,m,x)
   1    0      1.000000        1.000000e+00        1.000000e+00
  10    0      1.000000        9.999999e-01        1.000000e+00
  20    0      1.000000        1.000000e+00        1.000000e+00
   1    0      0.707107        7.071064e-01        7.071067e-01
  10    0      0.707107        1.151121e-01        1.151121e-01
  20    0      0.707107       -1.930652e-01       -1.930653e-01
   1    0      0.000000        0.000000e+00        0.000000e+00
  10    0      0.000000       -2.460938e-01       -2.460938e-01
  20    0      0.000000        1.761970e-01        1.761971e-01
   2    2      0.707107        1.500000e+00        1.500000e+00
  10    2      0.707107       -6.888429e+00       -6.888390e+00
  20    2      0.707107        8.423188e+01        8.423187e+01
   2    2      0.000000        3.000000e+00        3.000000e+00
  10    2      0.000000        2.707032e+01        2.707031e+01
  20    2      0.000000       -7.400273e+01       -7.400276e+01
  10   10      0.707107        2.046010e+07        2.046030e+07
  20   10      0.707107       -1.335506e+12       -1.335507e+12
  10   10      0.000000        6.547289e+08        6.547291e+08
  20   10      0.000000       -1.612053e+12       -1.612053e+12