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Mathematics of Computation

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Recurrence techniques for the calculation of Bessel functions

Authors: M. Goldstein and R. M. Thaler
Journal: Math. Comp. 13 (1959), 102-108
MSC: Primary 65.00
MathSciNet review: 0105794
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References [Enhancements On Off] (What's this?)

  • [1] British Association for the Advancement of Science, ``Bessel functions, Part II,'' Mathematical Tables, Cambridge University Press, 1952. An application of a recurrence technique to the calculation of $ {I_n}(x)$ is credited in the Introduction to J. C. P. Miller. An extension of this technique for use on high speed computers for the calculation of Bessel functions of integral and half integral order appeared in print after the completion of this manuscript. I. A. Stegun & M. Abramowitz, ``Generation of Bessel functions on high speed computers,'' MTAC, v. XI, 1957, p. 255.
  • [2] G. N. Watson, A Treatise on the Theory of Bessel Functions, Second Edition, Cambridge University Press, 1948, p. 139 and 369. MR 0010746 (6:64a)
  • [3] Y. L. Luke, ``Simple formulas for the evaluation of some higher transcendental functions,'' Journal of Math. and Phys., v. 34, 1956, p. 298-307. MR 0078047 (17:1138e)
  • [4] H. E. Fettis, ``Numerical calculation of certain definite integrals by Poisson 's summation formula,'' MTAC, v. IX, 1955, p. 85-92. MR 0072546 (17:302f)
  • [5] M. Goldstein & R. M. Thaler, ``Bessel functions for large arguments;'' MTAC, v. XII, 1958, p. 18-26. MR 0102906 (21:1691)
  • [6] M. Goldstein & M. Kresge, NU BES I, Share Distribution 469, Share Program Librarian, IBM, 590 Madison Avenue, New York 22, New York.

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Article copyright: © Copyright 1959 American Mathematical Society

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