Editing Divided differences (section)

===Peano form===
If <math>x_0<x_1<\cdots<x_n</math> and <math>n\geq 1</math>, the divided differences can be expressed as<ref>{{Cite book |last=Skof |first=Fulvia |url=https://books.google.com/books?id=ulUM2GagwacC&dq=This+is+called+the+Peano+form+of+the+divided+differences&pg=PA41 |title=Giuseppe Peano between Mathematics and Logic: Proceeding of the International Conference in honour of Giuseppe Peano on the 150th anniversary of his birth and the centennial of the Formulario Mathematico Torino (Italy) October 2-3, 2008 |date=2011-04-30 |publisher=Springer Science & Business Media |isbn=978-88-470-1836-5 |pages=40 |language=en}}</ref>
<math display="block">f[x_0,\ldots,x_n] = \frac{1}{(n-1)!} \int_{x_0}^{x_n} f^{(n)}(t)\;B_{n-1}(t) \, dt</math>
where <math>f^{(n)}</math> is the <math>n</math>-th [[derivative]] of the function <math>f</math> and <math>B_{n-1}</math> is a certain [[B-spline]] of degree <math>n-1</math> for the data points <math>x_0,\dots,x_n</math>, given by the formula
<math display="block">B_{n-1}(t) = \sum_{k=0}^n \frac{(\max(0,x_k-t))^{n-1}}{\omega'(x_k)}</math>

This is a consequence of the [[Peano kernel theorem]]; it is called the ''Peano form'' of the divided differences and <math>B_{n-1}</math> is the ''Peano kernel'' for the divided differences, all named after [[Giuseppe Peano]].