What's the polynomial function with a finite difference of 24 in the fourth degree
If the quartic polynomial
\(ax^{4}+bx^{3}+cx^{2}+dx+e\)
where a, b, c, d and e are constants with a not equal to zero
is tabulated with the x values h apart,
the fourth differences will be constant and equal to \(ah^{4}\times4!\) that is \(24ah^{4}\).
What you need then is for \(ah^{4}\) to be equal to 1.
So then if, for example, you have h = 1, you need to have a = 1, if h = 2 then a =1/16 etc..
The values of the other constants don't matter.
- Bertie
