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

*z*and real order

*v*, are investigated. Special attention is paid to the location of saddle points and their trajectories as

*v*varies.

**[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