The factorial in the denominator is included to perfectly cancel out the product of constants generated by repeatedly applying the power rule during differentiation. When you take the nth derivative of the polynomial part, the coefficient becomes n!, which cancels the n! in the denominator, leaving exactly the target derivative value.
Conditions: The function is n-times differentiable at the center point a.; n is a non-negative integer.
The factorial in the denominator is included to perfectly cancel out the product of constants generated by repeatedly applying the power rule during differentiation. When you take the nth derivative of the polynomial part, the coefficient becomes n!, which cancels the n! in the denominator, leaving exactly the target derivative value.
Conditions: The function is n-times differentiable at the center point a.; n is a non-negative integer.