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Integrals with a large parameter: Legendre functions of large degree and fixed order

Published online by Cambridge University Press:  24 October 2008

F. Ursell
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL

Abstract

Suppose that a function f(z, n) depends on a large parameter n. A proposed expression g(z, n) is an asymptotic approximation for f(z, n) if it can be shown that the error (i.e. the difference between f(z, n) and g(z, n)) is small of an appropriate order when n → ∞. Effective error bounds are particularly useful in numerical work with asymptotic expansions. Most of the existing derivations of error bounds involve complicated calculations.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

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