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On a non-regular parametric integral

Published online by Cambridge University Press:  14 November 2011

W. K. Hayman
W. K. Hayman
Affiliation:
Imperial College of Science and Technology, London
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Extract

Suppose that f(t, λ) is, for fixed t in an open interval (a, b), a regular (or analytic or holomorphic) function of λ, when λ lies in a domain D of the complex plane. We assume that f is integrable with respect to t for fixed λ ∈ D, and consider the parametric integral

By hypothesis F(λ) exists for λ ∈ D and Professor W. N. Everitt has asked whether F(λ) is necessarily regular as a function of λ.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 83 , Issue 3-4 , 1979 , pp. 185 - 188
Copyright
Copyright © Royal Society of Edinburgh 1979

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References

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4Titchmarsh, E. C.. The Theory of Functions, 2nd edn (Oxford: Clarendon, 1939).Google Scholar