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Mathematics of Computation

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Bessel functions for large arguments


Authors: M. Goldstein and R. M. Thaler
Journal: Math. Comp. 12 (1958), 18-26
MSC: Primary 65.00; Secondary 33.00
DOI: https://doi.org/10.1090/S0025-5718-1958-0102906-3
MathSciNet review: 0102906
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References [Enhancements On Off] (What's this?)

  • [1] W. E. Milne, ``The numerical determination of characteristic numbers,'' Phys. Rev., v. 35, 1930, p. 863-867.
  • [2] Harold Jeffreys, ``On certain approximate solutions of linear differential equations of the second order,'' London Math. Soc., Proc., v. 23, 1923, p. 428-436. The mathematical method first given by Jeffreys was independently derived in connection with an important physical problem by a. G. Wentzel, ``Eine Verallgemeinerung der Quantenbedingungen für die Zwecke der Wellen-mechanik,'' Zeits. f. Physik, v. 38, 1926, p. 518-529. b. H. A. Kramers, ``Wellenmechanik und halbzahlige Quantisierung,'' Zeits. f. Physik, v. 39, 1926, p. 828-840. c. L. Brillouin, ``La mécanique ondulatoire de Schrödinger; une méthode générale de résolution par approximations sucessives,'' Comptes Rendus, v. 183, 1926, p. 24-26. d. L. Brillouin, ``Remarques sur la mécanique ondulatoire,'' J. de Physique, v. 7, 1926, p. 353-368, and is commonly referred to as the JWKB approximation.

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DOI: https://doi.org/10.1090/S0025-5718-1958-0102906-3
Article copyright: © Copyright 1958 American Mathematical Society