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Some definite integrals of the product of two Bessel functions of the second kind: (order zero)


Author: M. L. Glasser
Journal: Math. Comp. 28 (1974), 613-615
MSC: Primary 33A40
MathSciNet review: 0344541
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Abstract: A new integral representation is derived for the expression $ {J_0}(z){J_0}(Z) + {Y_0}(z) \cdot {Y_0}(Z)$ and used to evaluate a number of integrals containing $ {Y_0}(ax){Y_0}(bx)$. A supplementary table of integrals involving the function $ {K_0}(x)$ in the integrand appears in the microfiche section of this issue.


References [Enhancements On Off] (What's this?)

  • [1] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746
  • [2] Yudell L. Luke, Integrals of Bessel functions, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1962. MR 0141801
  • [3] G. Z. Forristall and J. D. Ingram, Evaluation of distributions useful in Kontorovich-Lebedev transform theory, SIAM J. Math. Anal. 3 (1972), 561–566. MR 0313805
  • [4] A. Erdélyi et al., Tables of Integral Transforms. Vol. 2, McGraw-Hill, New York, 1954, p. 173. MR 16, 468.
  • [5] Ibid, p. 380.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1974-0344541-7
Keywords: Bessel function, definite integrals
Article copyright: © Copyright 1974 American Mathematical Society