Some definite integrals of the product of two Bessel functions of the second kind: (order zero)
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- by M. L. Glasser PDF
- Math. Comp. 28 (1974), 613-615 Request permission
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
- G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746
- Yudell L. Luke, Integrals of Bessel functions, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1962. MR 0141801
- 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 313805, DOI 10.1137/0503055 A. Erdélyi et al., Tables of Integral Transforms. Vol. 2, McGraw-Hill, New York, 1954, p. 173. MR 16, 468. Ibid, p. 380.
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Math. Comp. 28 (1974), 613-615
- MSC: Primary 33A40
- DOI: https://doi.org/10.1090/S0025-5718-1974-0344541-7
- MathSciNet review: 0344541