defmodule Gamma do
  @a [ 1.00000_00000_00000_00000,  0.57721_56649_01532_86061, -0.65587_80715_20253_88108,
      -0.04200_26350_34095_23553,  0.16653_86113_82291_48950, -0.04219_77345_55544_33675,
      -0.00962_19715_27876_97356,  0.00721_89432_46663_09954, -0.00116_51675_91859_06511,
      -0.00021_52416_74114_95097,  0.00012_80502_82388_11619, -0.00002_01348_54780_78824,
      -0.00000_12504_93482_14267,  0.00000_11330_27231_98170, -0.00000_02056_33841_69776,
       0.00000_00061_16095_10448,  0.00000_00050_02007_64447, -0.00000_00011_81274_57049,
       0.00000_00001_04342_67117,  0.00000_00000_07782_26344, -0.00000_00000_03696_80562,
       0.00000_00000_00510_03703, -0.00000_00000_00020_58326, -0.00000_00000_00005_34812,
       0.00000_00000_00001_22678, -0.00000_00000_00000_11813,  0.00000_00000_00000_00119,
       0.00000_00000_00000_00141, -0.00000_00000_00000_00023,  0.00000_00000_00000_00002 ]
     |> Enum.reverse
  def taylor(x) do
    y = x - 1
    1 / Enum.reduce(@a, 0, fn a,sum -> sum * y + a end)
  end
end

Enum.each(Enum.map(1..10, &(&1/3)), fn x ->
  :io.format "~f  ~18.15f~n", [x, Gamma.taylor(x)]
end)
