4-ary mekso operator: Taylor expansion/polynomial term; for ordered input (X_{1, X}, output is the X_{3}th Taylor polynomial term of at-least-X_{3}-smooth function X_{2} which was expanded around point X_{4} and which is evaluated at point X_{1}, namely (1/(X_{3!)) × (D^X}.

All of the usual assumptions must apply in order to be well-defined. X_{3} must be a nonnegative integer. X_{2} must be a function with at least X_{3} derivatives on the interval disc/interval defined by X_{1} and X_{4} such that said derivative takes values for which the other operators make sense (and finity is usually assumed). X_{1} and X_{4} must be elements of the domain of X_{2} (and the X_{3}th derivative thereof in the latter case). The notation "(D^X_{3(X}" represents the X_{3}th derivative of X_{2}, applied to X_{4}; the "!" notation represents the factorial.