apple-0.3.0.0: math/fcdf.apple

λn.λm.λx.
{
  incΒ ← λz.λa.λb.
    {
      f21 ← λa0.λa1.λb.λz.
        {
          rf ← [(*)/ₒ 1 (𝒻 x (x+y-1) (⌊y))]; fact ← rf 1;
          Σ ← λN.λa. (+)/ₒ 0 (a'(⍳ 0 N 1));
          term ← λn. {nn⟜ℝ n; ((rf a0 nn)*(rf a1 nn)%(rf b nn))*((z^n)%(fact nn))};
          Σ 30 term
        };
      ((z**a)%a)*f21 a (1-b) (a+1) z
    };
  Β ← λx.λy.
    {
      gammaln ⟜ λz.
        {
          zz ⟜ z-1;
          c0 ← 0.999999999999997092;
          𝛾 ← 607%128;
          coeffs ← ⟨ 57.1562356658629235
                   , _59.5979603554754912
                   , 14.1360979747417471
                   , _0.491913816097620199
                   , 0.339946499848118887e-4
                   , 0.465236289270485756e-4
                   , _0.983744753048795646e-4
                   , 0.158088703224912494e-3
                   , _0.210264441724104883e-3
                   , 0.217439618115212643e-3
                   , _0.164318106536763890e-3
                   , 0.844182239838527433e-4
                   , _0.261908384015814087e-4
                   , 0.368991826595316234e-5
                   ⟩;
          ss ← (+)/ ([y%(zz+ℝ x)]`(⍳ 1 14 1) coeffs);
          (((zz+0.5)*_.(zz+𝛾+0.5))-(zz+𝛾+0.5))+_.((√(2*𝜋))*(c0+ss))
        };
      e:(gammaln x+gammaln y-gammaln (x+y))
    };
  I ← λz.λa.λb. incΒ z a b%Β a b;
  I ((n*x)%(m+n*x)) (n%2) (m%2)
}