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

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]**Andrés Cruz and Javier Sesma,*Modulus and phase of the reduced logarithmic derivative of the cylindrical Bessel function*, Math. Comp.**35**(1980), no. 152, 1317–1324. MR**583509**, 10.1090/S0025-5718-1980-0583509-5**[2]**Andrés Cruz and Javier Sesma,*Zeros of the Hankel function of real order and of its derivative*, Math. Comp.**39**(1982), no. 160, 639–645. MR**669655**, 10.1090/S0025-5718-1982-0669655-8**[3]**Henry E. Fettis, James C. Caslin, and Kenneth R. Cramer,*Saddle points of the complementary error function*, Math. Comp.**27**(1973), 409–412. MR**0326992**, 10.1090/S0025-5718-1973-0326992-9**[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]**Herbert E. Salzer,*Complex zeros of the error function*, J. Franklin Inst.**260**(1955), 209–211. MR**0071880**

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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