See also Bürmann's Theorem ,
Maclaurin Series ,
Schur-Jabotinsky
Theorem ,
Taylor Series ,
Teixeira's
Theorem
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References Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
New York: Dover, p. 14, 1972. Goursat, E. A
Course in Mathematical Analysis, Vol. 2: Functions of a Complex Variable &
Differential Equations. New York: Dover, pp. 106 and 120, 1959. Henrici,
P. "An Algebraic Proof of the Lagrange-Burmann Formula." J. Math. Anal.
Appl. 8 , 218-224, 1964. Henrici, P. "The Lagrange-Bürmann
Theorem." §1.9 in Applied
and Computational Complex Analysis, Vol. 1: Power Series-Integration-Conformal
Mapping-Location of Zeros. New York: Wiley, pp. 55-65, 1988. Joni,
S. A. "Lagrange Inversion in Higher Dimensions and Umbral Operators."
J. Linear Multi-Linear Algebra 6 , 111-121, 1978. Lagrange,
J.-L. "Nouvelle méthode pour résoudre les problèmes indéterminés
en nombres entiers." Mém. de l'Acad. Roy. des Sci. et Belles-Lettres
de Berlin 24 , 1770. Reprinted in Oeuvres de Lagrange, tome 2, section
deuxième: Mémoires extraits des recueils de l'Academie royale des sciences
et Belles-Lettres de Berlin. Paris: Gauthier-Villars, pp. 655-726, 1868. Moulton,
F. R. An
Introduction to Celestial Mechanics, 2nd rev. ed. New York: Dover, p. 161,
1970. Popoff, M. "Sur le reste de la série de Lagrange."
Comptes Rendus Herbdom. Séances de l'Acad. Sci. 53 , 795-798,
1861. Roman, S. "The Lagrange Inversion Formula." §5.2.
in The
Umbral Calculus. New York: Academic Press, pp. 138-140, 1984. Whittaker,
E. T. and Watson, G. N. "Lagrange's Theorem." §7.32 in A
Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University
Press, pp. 132-133, 1990. Williamson, B. "Remainder in Lagrange's
Series." §119 in An
Elementary Treatise on the Differential Calculus, Containing the Theory of Plane
Curves, with Numerous Examples, 9th ed. London: Longmans, pp. 158-159,
1895. Referenced on Wolfram|Alpha Lagrange Inversion Theorem
Cite this as:
Weisstein, Eric W. "Lagrange Inversion Theorem."
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