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Modulus and phase of the reduced logarithmic derivative of the Hankel function


Authors: Andrés Cruz and Javier Sesma
Journal: Math. Comp. 41 (1983), 597-605
MSC: Primary 33A40; Secondary 65H05, 81F10
DOI: https://doi.org/10.1090/S0025-5718-1983-0717705-3
MathSciNet review: 717705
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Abstract | References | Similar Articles | Additional Information

Abstract: The modulus and phase of the reduced logarithmic derivative of the Hankel function

$\displaystyle zH_v^{(1)}{}' (z)/H_v^{(1)}(z)$

for complex variable z and real order v, are investigated. Special attention is paid to the location of saddle points and their trajectories as v varies.

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

  • [1] A. Cruz & J. Sesma, "Modulus and phase of the reduced logarithmic derivative of the cylindrical Bessel function," Math. Comp., v. 35, 1980, pp. 1317-1324. MR 583509 (82b:33010)
  • [2] A. Cruz & J. Sesma, "Zeros of the Hankel function of real order and of its derivative," Math. Comp., v. 39, 1982, pp. 639-645. MR 669655 (83j:33005)
  • [3] H. E. Fettis, J. C. Caslin & K. R. Cramer, "Saddle points of the complementary error function," Math. Comp., v. 27, 1973, pp. 409-412. MR 0326992 (48:5334)
  • [4] F. W. J. Olver, "Bessel functions of integer order," Handbook of Mathematical Functions (M. Abramowitz & I. A. Stegun, Eds.), Dover, New York, 1965, pp. 355-433.
  • [5] H. E. Salzer, "Complex zeros of the error function," J. Franklin Inst., v. 260, 1955, pp. 209-211. MR 0071880 (17:197d)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1983-0717705-3
Keywords: Hankel functions, modulus and phase of the reduced logarithmic derivative, quantum potential scattering
Article copyright: © Copyright 1983 American Mathematical Society

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