New explicit formulas for the $n$th derivative of composite functions.
Pavel G. Todorov
Source: Pacific J. Math. Volume 92, Number 1
(1981), 217-236.
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Permanent link to this document: http://projecteuclid.org/euclid.pjm/1102737515
Zentralblatt MATH identifier: 0459.30014
Mathematical Reviews number (MathSciNet): MR618059
References
[1] J. Bertrand, Traite de calcul dierentiel et de calcul integral {Premiere partie--Calcul differentiel), Gauthier-Villars, Paris, 1864.
[2] L. Comtet, Advanced Combinatorics (The Art oj Finite and Infinite Expansions), D. Reidel Publishing Co., Dordrecht-Holland/Boston-U.S.A. 1974.
Mathematical Reviews (MathSciNet): MR57:124
Zentralblatt MATH: 0283.05001
[3] L. Comtet, Polynomes de Bell et formue explicite des derivees successives d'une fonction implicite, C. R. Acad. Sc. Paris, 267-A (1968), 457-460.
Mathematical Reviews (MathSciNet): MR38:2030
Zentralblatt MATH: 0165.02701
[4] L. Comtet,Une formule explicite pour les puissances successivesde Voperateur de deriva- tion de Lie, C. R. Acad. Sc Paris, 276-A (1973), 165-168.
Mathematical Reviews (MathSciNet): MR47:6503
Zentralblatt MATH: 0252.05002
[5] Faa di Bruno, Sullo sviluppo delle funzioni,Annali di Scienze Matematiche et Fisiche di Tortoloni, 6 (1855), 479-480.
[6] Faa di Bruno, Note sur une nouvelle formule de calcul difterentiel, Quarterly J. Math., 1 (1857), 359-360.
[7] H. Gould, Explicit formulas for Bernoulli numbers, Amer. Math. Monthly, 79 (1972), 44-51.
Mathematical Reviews (MathSciNet): MR46:5229
Zentralblatt MATH: 0227.10010
[8] P. Henrici,Appliedand Computational Complex Analysis, ed. J. Wiley and Sons, Inc., New York-London-Sydney-Tor onto, Vol. 1, 1974.
Mathematical Reviews (MathSciNet): MR51:8378
Zentralblatt MATH: 0313.30001
[9] V. F. Ivanoff, Problem 4782, Amer. Math. Monthly, 65 (1958), 212.
[10] Charles Jordan, Calculus of Finite Differencse, 3rd ed., Chelsea Publishing Co., Inc., New York 1965, (repr. 1979).
Mathematical Reviews (MathSciNet): MR32:1463
Zentralblatt MATH: 0154.33901
[11] F. G. Kravchenko, Representations of roots of polynomial in the form of power series and infinite determinants, Vychislitenaya i prikladnaya matematika, Izdatestvo Kievskogo Universiteta, Kiev, No. 4 (1967), 70-89 (Russian: Summary in English).
[12] M. McKiernan, On the nth derivative of composite functions, Amer. Math. Monthly, 63 (1956), 331-333.
Mathematical Reviews (MathSciNet): MR17:953e
Zentralblatt MATH: 0070.05701
[13] A. M. Ostrowski, Solution of Equations and Systems of Equations, 2nd ed., Academic Press, New York, 1966.
Mathematical Reviews (MathSciNet): MR35:7575
[14] D. Pandres, On higher ordered differentiation, Amer. Math. Monthly, 64 (1957), 566-572.
Mathematical Reviews (MathSciNet): MR19:534f
Zentralblatt MATH: 0079.01304
[15] J. Riordan, Derivatives of composite functions, Bull. Amer. Math. Soc, 52 (1946), 664-667.
Mathematical Reviews (MathSciNet): MR8:200a
Zentralblatt MATH: 0063.06505
[16] J. Riordan, An Introduction to Combinatorial Analysis, ed. J. Wiley and Sons, Inc., New York-London, 1958.
Mathematical Reviews (MathSciNet): MR20:3077
Zentralblatt MATH: 0436.05001
[17] E. Stamm, A Contribution to Differential Calculus in Banach Spaces: The Combina- torial Mechanisms of Higher Derivatives, ed. Forschungsinstitut fur Mathematik ETH Zurich and Department of Mathematics, University of Toronto, August, 1973.
[18] P. G. Todorov, New explicit formulas for the coefficients of p-symmetricfunctions, Notices Amer. Math. Soc, 25 No. 6 (1978). A-592, Abstract 78T-B186.
Mathematical Reviews (MathSciNet): MR81g:30021
Zentralblatt MATH: 0425.30007
[19] P. G. Todorov, New explicit formulas for the coefficients of p-symmetric functions, Proc. Amer. Math. Soc, 77 No. 1 (1979), 81-86.
Mathematical Reviews (MathSciNet): MR81g:30021
Zentralblatt MATH: 0425.30007
[20] P. G. Todorov, New explicit formulas for the nth derivative of composite functions, Notices Amer. Math. Soc, 25, No. 7 (1978), A-699, Abstract 78T-B199.
Mathematical Reviews (MathSciNet): MR85h:26008
[21] A. B. Turowicz, Sur les derivees d'ordre superieur d'une fonction inverse, Colloquium Mathematicum, 7, No. 1 (1959), 83-87.
Mathematical Reviews (MathSciNet): MR22:5703
Zentralblatt MATH: 0090.27403
Pacific Journal of Mathematics
