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On an Asymptotic Integral

Published online by Cambridge University Press:  20 January 2009

L. C. Hsu
L. C. Hsu
Affiliation:
King's College, Aberdeen.
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1. This note gives an asymptotic evaluation of an integral of the form

as n tends to infinity, where is a sequence of real-valued functions. The theorem to be established is a natural extension of B. Levi's generalised Laplace-Darboux theorem (1, 341-51); it gives a rule for evaluating a wider class of asymptotic integrals.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 10 , Issue 3 , January 1956 , pp. 141 - 144
Copyright
Copyright © Edinburgh Mathematical Society 1956

References

REFERENCES

[1] Levi, Beppo, Publ. Inst., Math. Univ. Nac. Litoral, 6 (1946).Google Scholar
[2] Laplace, P. S., Oeuvres, t. 7, p. 89. Paris (1886).Google Scholar
[3] Darboux, G., Jour, de Math. (3), 4 (1878).Google Scholar
[4] Pólya, G. and Szegö, G., Aufgaben und Lehrsätze aus der Analysis, Bd. 1, e. 78 (1925).Google Scholar