Category:Examples of Forward Difference Operator

This category contains examples of Forward Difference Operator.

$\Delta \map f {x_i} := \map f {x_{i + 1} } - \map f {x_i}$

for $i = 0, 1, 2, \ldots, n - 1$

$\ds \map {\Delta^2 f} {x_i}$

$=$

$\ds \map \Delta {\map {\Delta f} {x_i} }$

$\ds $

$=$

$\ds \Delta \map f {x_{i + 1} } - \Delta \map f {x_i}$

$\ds $

$=$

$\ds \map f {x_{i + 2} } - 2 \Delta \map f {x_{i + 1} } + \Delta \map f {x_i}$

for $i = 0, 1, 2, \ldots, n - 2$

$\ds \map {\Delta^k f} {x_i}$

$=$

$\ds \map \Delta {\map {\Delta^{k - 1} f} {x_i} }$

$\ds $

$=$

$\ds \Delta^{k - 1} \map f {x_{i + 1} } - \Delta^{k - 1} \map f {x_i}$

$\ds $

$=$

$\ds \sum_{s \mathop = 0}^k \paren {-1}^{k - s} \dbinom k s y_{i + s}$

for $i = 0, 1, 2, \ldots, n - k$

Pages in category "Examples of Forward Difference Operator"

The following 4 pages are in this category, out of 4 total.