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A property of certain even integral functions

Published online by Cambridge University Press:  24 October 2008

F. Monticelli
Affiliation:
Edison-Azienda Chimica, Portomarghera, Venice (Italy)

Extract

In some problems where sine, cosine or Bessel functions are involved (e.g. (l), p. 35 et seq.), one has to satisfy certain initial conditions so that one obtains relations of the type

where t is a real parameter such that |t| < 1, and ±αn(n = 1, 2, …) are real simple zeros of an even or odd integral function f(z), being z = x + iy. An's are coefficients to be determined and, of course, ±ω is a real number that is not a zero of f(z).

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCE

(1)Tranter, C. J.Integral transforms in mathematical physics (Methuen; London, 1951).Google Scholar