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A method for the determination of converging factors, applied to the asymptotic expansions for the parabolic cylinder functions

Published online by Cambridge University Press:  24 October 2008

J. C. P. Miller
J. C. P. Miller
Affiliation:
University Mathematical LaboratoryCambridge
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Extract

1. The method of converging factors, for hastening the convergence of slowly convergentseries and improving the accuracy of asymptotic expansions, was introduced by J. R. Airey and is well known to computers (see Airey(1) and Rosser(2)). The principle is as follows. It is required to compute a quantity which is expressed as an infinite series

The series may be either convergent or asymptotic and divergent.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 48 , Issue 2 , April 1952 , pp. 243 - 254
Copyright
Copyright © Cambridge Philosophical Society 1952

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References

REFERENCES

(1)Airey, J. R.Phil. Mag. (7), 24 (1937), 521–52.CrossRefGoogle Scholar
(2)Rosser, J. B.Bur. Stand. J. Res., Wash., 46 (1951), 56–64.CrossRefGoogle Scholar
(3)Stieltjes, M. T.Ann. sci. Éc. norm. sup. Paris (3), 3 (1886), 201–58.CrossRefGoogle Scholar