"Counting in their heads"  1895 oil painting

08132020, 03:50 PM
Post: #22




RE: "Counting in their heads"  1895 oil painting
There is also the Faulhaber polynomials, with sumofpowers formula as function of triangular number.
Let \(\large t = \binom{x}{2},\;{s_{2m} \over (2x1)t}\) and \(\large {s_{2m+1} \over t^2}\) are polynomial of t, degree m1 Example, get s4(x) and s5(x) in terms of t, using divided difference. Note: we start from x=2, instead of 0, to avoid dividebyzero issue. Code: x s4(x)  t s4/(2xtt) divideddiff Redo previous example, using horners rule for the difference. Code: lua> a,b = 50, 151  next line replaced with t's 

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