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Lagrange's theorem for weak functions of several variables

Published online by Cambridge University Press:  26 February 2010

M. D. Quinn
Affiliation:
Department of Mathematics, The University of Dundee.
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Summary

This paper contains a derivation of Lagrange's expansion with remainder for a weak function of several independent variables each satisfying an implicit relation. We also provide necessary and sufficient conditions for the associated infinite series expansion.

MSC classification

Type
Research Article
Copyright
Copyright © University College London 1978

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References

1.Chaundy, T.. The differential calculus (Oxford University Press, 1935).Google Scholar
2.Good., I. J.Generalizations to several variables of Lagrange's expansion, with applications to stochastic processes”, Proc. Cam. Phil. Soc, 56 (1960), 367380.CrossRefGoogle Scholar
3.Goursat, E.. Cours d'analyse mathématique, 5th ed., Vols. I and II (Gauthier-Villars, 1927 and 1929).Google Scholar
4.Jones., D. S.Lagrange's Theorem for weak functions”, Mathematika, 13 (1966), 158171.CrossRefGoogle Scholar
5.Jones., D. S.Generalised functions (McGraw-Hill, 1966).Google Scholar
6.Mirsky, L.. An introduction to linear algebra (Oxford, 1955).Google Scholar
7.Sack., R. A.Interpretation of Lagrange's expansion and its generalizations to several variables as integration formulas”, J. SIAM. Appl. Math., 13 (1965), 4759.CrossRefGoogle Scholar
8.Whittaker, E. T. and Watson., G. N.Modern analysis (Cambridge University Press, 1927).Google Scholar