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Asymptotic distribution of the zeros of certain Lagrange interpolants

Published online by Cambridge University Press:  20 January 2009

M. A. Bokhari  and
M. Iqbal
M. A. Bokhari
Affiliation:
Department of Mathematical SciencesKing Fahd University of Petroleum and MineralsDhahran 31261, Saudi Arabia E-Mail: FACL049@SAUPM00.BITNET.
M. Iqbal
Affiliation:
Department of Mathematical SciencesKing Fahd University of Petroleum and MineralsDhahran 31261, Saudi Arabia E-Mail: FACL049@SAUPM00.BITNET.
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Abstract

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We consider rational functions of the form fm(z) = zm/(z – p) which are analytic in |z|<p, p>1, and establish that the asymptotic distribution of the zeros of their Taylor sections and Lagrange interpolants at uniformly distributed nodes is similar. This notion is also illustrated computationally. We conjecture that a similar result can be expected for any function analytic in |z| < p.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , Issue 1 , February 1995 , pp. 99 - 106
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

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