The differential mean value of divided differences |
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| Authors: | Ulrich Abel Mircea Ivan |
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| Institution: | a Fachbereich MND, Fachhochschule Giessen-Friedberg, University of Applied Sciences, Wilhelm-Leuschner-Straße 13, 61169 Friedberg, Germany
b Department of Mathematics, Technical University of Cluj-Napoca, Str. C. Daicoviciu 15, 400020 Cluj-Napoca, Romania |
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| Abstract: | The paper deals with the asymptotic behaviour of the differential mean value of divided differences as the interval shrinks to zero by presenting an asymptotic expansion. The coefficients are given by a recurrence formula. For a wide class of analytic functions the differential mean value can be represented by a convergent sum. Our results generalize two recent theorems by Powers, Riedel and Sahoo R.C. Powers, T. Riedel, P.K. Sahoo, Limit properties of differential mean values, J. Math. Anal. Appl. 227 (1998) 216-226]. |
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| Keywords: | Divided differences Differentiation Mean value theorems Asymptotic approximations Asymptotic expansions |
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