Taylor series based finite difference approximations of higher-degree derivatives

A new type of Taylor series based finite difference approximations of higher-degree derivatives of a function are presented in closed forms, with their coefficients given by explicit formulas for arbitrary orders. Characteristics and accuracies of presented approximations and already presented central difference higher-degree approximations are investigated by performing example numerical differentiations. It is shown that the presented approximations are more accurate than the central difference approximations, especially for odd degrees. However, for even degrees, central difference approximations become attractive, as the coefficients of the presented approximations of even degrees do not correspond to equispaced input samples.