Finite Differences

FINITE DIFFERENCES

Consider the arguments x₀ , x₁ , x₂ , , x_n and the entries y₀ , y₁ , y₂ , , y_n . y =f (x) be a function of x. Let us assume that the values of x are in increasing order and equally spaced with a space length h. Then the values of x may be taken to be x₀ , x₀+h , x₀+2h ,.... , x₀+nh          and the function assumes the values f (x₀ ), f (x₀ + h ), f (x ₀ + 2h), , f (x₀ + nh) . Here we study some of the finite differences of the function y = f ( x)