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Utilitas Mathematica

Volumn 61, Issue , 2002, Pages 97-106

The generalized chain rule of differentiation with historical notes

(1) Gould, H W a

a WEST VIRGINIA UNIVERSITY (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035982718 PISSN: 03153681 EISSN: None Source Type: Journal
DOI: None Document Type: Article

Times cited : (7)

References (19)

1
- 0000583920
- Sur la différentiation des fonctions de fonctions
- Actually, the author is given by initials only, as T.A., Ancien élève de l'École Polytechnique. But he was later identified by name on p. 256 in the Index to the Royal Society Cataloque of Scientific Papers (1800-1900), published in 1908
- (1850) Nouv. Ann, Math. , vol.9 , Issue.1 , pp. 119-125
- Anne, T.¹

2
- 0001164156
- Sur la differentiation des fonctions de fonctions, Séries de Burmann, de Lagrange, de Wronski
- (1852) Nouv. Ann, Math. , vol.11 , Issue.1 , pp. 376-385
- Anne, T.¹

3
- 0000794806
- Exponential polynomials
- r
- (1934) Annals of Mathematics , vol.35 , pp. 258-277
- Bell, E.T.¹

4
- 0001305977
- Sullo sviluppo delle funzioni
- (1855) Annali di Scienze Matematiche e Fisiche di Tortolini , vol.6 , pp. 479-480
- De Bruno, F.¹

5
- 0001666357
- Note sur une nouvelle formule de calcul différential
- Oxford, He notes that the paper was written at Paris 17 Dec. 1855
- (1857) Quarterly Journal of Mathematics , vol.1 , pp. 359-360
- De Bruno, F.¹

6
- 0005335643
- Henry Holt and Co., N.Y., Second edition, xii + 482 pp. See Appendix, Note 4
- (1902) An Elementary textbook of the Differential and Integral Calculus
- Echols, W.H.¹

7
- 0005328661
- Master's Thesis, University of Virginia. iv + 66 pp.
- (1956) The Stirling Numbers and Generalized Difference Expansions
- Gould, H.W.¹

8
- 84968468424
- Stirling number representation problems
- MR 22, #5586
- (1960) Proc. Amer. Math. Soc. , vol.11 , pp. 447-451
- Gould, H.W.¹

9
- 84968491152
- The Lagrange interpolation formula and Stirling numbers
- MR 22, #5588
- (1960) Proc. Amer. Math. Soc. , vol.11 , pp. 421-425
- Gould, H.W.¹

10
- 78650749201
- Operational formulas connected with two generalizations of Hermite polynomials
- r)
- (1962) Duke Math. Journal , vol.29 , pp. 51-63
- Gould, H.W.¹ Hopper, A.T.²

11
- 0003723504
- Published by the author, Morgantown, WV, MR 50, #6879
- (1972) Combinatorial Identities, A Standardized Set of Tables Listing 500 Binomial Coefficient Summations, Revised Edition
- Gould, H.W.¹

12
- 0005276831
- Series expansions of means
- (1984) Journal of Math. Anal. and Appl. , vol.101 , pp. 611-621
- Gould, H.W.¹ Mays, M.E.²

13
- 25744472558
- In preparation. Will have about 150 items, tracing the history of the formulas of Theodore Anne, Faà de Bruno, and Reinhold Hoppe
- Bibliography on the chain rules for higher derivatives of composite functions
- Gould, H.W.¹

14
- 0002545094
- Über independente Darstellung der höheren Differentialquotienten und den Gebrauch des Summenzeichens
- r) by a convenient formula
- (1846) Journal für die reine und annewandte Mathematik (Crelle's Journal) , vol.33 , pp. 78-89
- Hoppe, R.¹

15
- 0002596653
- Über independente Darstellung der höheren Differentialquotienten
- (1871) Mathematische Annalen , vol.4 , pp. 85-87
- Hoppe, R.¹

16
- 0005272158
- Master's Thesis, West Virginia University
- (1961) Generalized Hermite polynomials
- Hopper, A.T.¹

17
- 84966222362
- Derivatives of composite functions
- (1946) Bull. Amer. Math. Soc. , vol.52 , pp. 664-667
- Riordan, J.¹

18
- 0003862964
- John Wiley and Sons, Inc., N.Y. Note esp. where he uses Bell polynomials to get Faà de Bruno's formula
- (1958) An Introduction to Combinatorial Analysis , pp. 34-38
- Riordan, J.¹

19
- 0004261506
- Univ. of Pennsylvania Press, Philadelphia, Reprinted by Chelsea Publications, N.Y., with corrections by H.W. Gould
- (1924) An Introduction to the Operations with Series
- Schwatt, I.J.¹

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