Note that the Lagrange remainder is also sometimes taken to refer to the remainder when terms
up to the st
power are taken in the Taylor series, and that a
notation in which ,
,
and
is sometimes used (Blumenthal 1926; Whittaker and Watson 1990, pp. 95-96).

Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
New York: Dover, 1972.Beesack, P. R. "A General Form of the
Remainder in Taylor's Theorem." Amer. Math. Monthly73, 64-67,
1966.Blumenthal, L. M. "Concerning the Remainder Term in Taylor's
Formula." Amer. Math. Monthly33, 424-426, 1926.Firey,
W. J. "Remainder Formulae in Taylor's Theorem." Amer. Math. Monthly67,
903-905, 1960.Fulks, W. Advanced
Calculus: An Introduction to Analysis, 4th ed. New York: Wiley, p. 137,
1961.Nicholas, C. P. "Taylor's Theorem in a First Course."
Amer. Math. Monthly58, 559-562, 1951.Poffald, E. I.
"The Remainder in Taylor's Formula." Amer. Math. Monthly97,
205-213, 1990.Whittaker, E. T. and Watson, G. N. "Forms
of the Remainder in Taylor's Series." §5.41 in A
Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University
Press, pp. 95-96, 1990.