Hankel Transforms

  • B. Davies
Part of the Applied Mathematical Sciences book series (AMS, volume 25)


Bessel functions have frequently occurred in our investigations of the Laplace and Fourier transforms; indeed, we could rewrite most of the formulas we have derived in terms of Bessel functions of order ±1/2, since (2x/π)1/2K1/2 (x) = exp(−x), with similar relations for sin(x) and cos(x).


Bessel Function Hankel Function Thin Elastic Plate Fourier Cosine Initial Temperature Distribution 
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  1. 1.
    For example, Sneddon (1972).Google Scholar
  2. 2.
    Lommnl’s integral is for any pair of cylinder functions Uν and Vν [Watson (1958), p. 134]. It may be used to obtain results such asGoogle Scholar
  3. 3.
    If Fν(k) is analytic in a region of the complex plane containing a ≤ k ≤ b, then we replace (3) byGoogle Scholar
  4. 4.
    In particular the case b → ∞ is easy to handle. Also, if the interval 0 ≤ x ≤ ∞ can be split up into a finite number of subintervals in each of which the condition of MacRobert’s proof applies, then the proof is easily generalized. This covers most functions which arise in applications.Google Scholar
  5. 5.
    We have chosen the constants 2π in a more symmetrical way than in (11.1) and (11.2).Google Scholar
  6. 6.
    Another transform is obtained from the choice.Google Scholar

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • B. Davies
    • 1
  1. 1.Department of MathematicsThe Australian National UniversityCanberraAustralia

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