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Cross-references: divided difference table, argument, interpolating functions, vanish, order, polynomial, permutations, invariant, properties, numbers, function, complex, real
There are 11 references to this entry.
This is version 7 of divided difference, born on 2004-10-04, modified 2007-03-08.
Object id is 6288, canonical name is DividedDifference.
Accessed 3535 times total.
Classification:
| AMS MSC: | 39A70 (Difference and functional equations :: Difference equations :: Difference operators) |
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Pending Errata and Addenda
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![$\displaystyle \Delta^1 f [x_0, x_1]$](http://images.planetmath.org:8080/cache/objects/6288/l2h/img4.png "$\displaystyle \Delta^1 f [x_0, x_1]$"){kind=small}
![$\displaystyle \Delta^{n+1} f [x_0, x_1,\ldots, x_{n+1}]$](http://images.planetmath.org:8080/cache/objects/6288/l2h/img6.png "$\displaystyle \Delta^{n+1} f [x_0, x_1,\ldots, x_{n+1}]$"){kind=small}
![$\displaystyle = {\Delta^n f [x_1, x_2, \ldots ,x_{n+1}] - \Delta^n f [x_0, x_2 ,\ldots, x_{n+1}] \over x_1 - x_0}$](http://images.planetmath.org:8080/cache/objects/6288/l2h/img7.png "$\displaystyle = {\Delta^n f [x_1, x_2, \ldots ,x_{n+1}] - \Delta^n f [x_0, x_2 ,\ldots, x_{n+1}] \over x_1 - x_0}$")
![$\displaystyle \Delta^0 f [x_0] = f[x_0] $](http://images.planetmath.org:8080/cache/objects/6288/l2h/img10.png "$\displaystyle \Delta^0 f [x_0] = f[x_0] $"){kind=small}
![$\displaystyle \Delta^{n+1} f [x_0, x_1,\ldots, x_{n+1}] = {\Delta^n f [x_1, x_2, \ldots ,x_{n+1}] - \Delta^n f [x_0, x_1 ,\ldots, x_{n}] \over x_{n+1} - x_0} $](http://images.planetmath.org:8080/cache/objects/6288/l2h/img24.png "$\displaystyle \Delta^{n+1} f [x_0, x_1,\ldots, x_{n+1}] = {\Delta^n f [x_1, x_2, \ldots ,x_{n+1}] - \Delta^n f [x_0, x_1 ,\ldots, x_{n}] \over x_{n+1} - x_0} $")