apple-0.3.0.0: math/tcdf.apple

λx.λν.
{
  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+itof x)]`(⍳ 1 14 1) coeffs);
    (((zz+0.5)*_.(zz+𝛾+0.5))-(zz+𝛾+0.5))+_.((√(2*𝜋))*(c0+ss))
  };
  Γ ⟜ [ℯ(gammaln x)];
  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 50 term
  };
  0.5+x*Γ(0.5*(ν+1))%((√(𝜋*ν))*Γ(ν*0.5))*f21 ½ ((ν+1)%2) 1.5 (_(x^2%ν))
}