Accurate Normal Distribution for the HP67/97

[Albert Chan]

(12-03-2018 12:44 AM)Albert Chan Wrote:  Sum it all, and ignore O(h⁴) terms, we get:

x correction = h = t + x/2 · t² + (2x²+1)/6 · t³

I am too lazy to do 4th order correction by hand. Using Mathematica:

z = c Exp[-x²/2];
D[z, {x, 3}] / z ==> -x (-3 + x²)

t = h - (x/2) h^2 + (x²-1)/6 h^3 - x*(x²-3)/24 h^4;

mess = Expand[t + (x/2) t^2 + (2x²+1)/6 t^3 + k t^4];

Simplify[(mess /. h^4 -> c /. h -> 0) / c] ==> k - 1/24 x(7 + 6x²)

4th order x correction = t + x/2 · t² + (2x²+1)/6 · t³ + x*(6x²+7)/24 t⁴