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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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 | References | Similar Articles | Additional Information

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, 2nd ed., Cambridge Univ. Press, Cambridge; Macmillan, New York, 1944. MR 6, 64. MR 0010746 (6:64a)
  • [2] Y. L. Luke, Integrals of Bessel Functions, McGraw-Hill, New York, 1962. MR 25 #5198. MR 0141801 (25:5198)
  • [3] See, e.g., G. Z. Forristall & J. D. Ingram, SIAM J. Math. Anal., v. 3, 1972, p. 561. MR 0313805 (47:2359)
  • [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
PII: S 0025-5718(1974)0344541-7
Keywords: Bessel function, definite integrals
Article copyright: © Copyright 1974 American Mathematical Society