Zeros of the Hankel function of real order and of its derivative

Authors:
Andrés Cruz and Javier Sesma

Journal:
Math. Comp. **39** (1982), 639-645

MSC:
Primary 33A40

MathSciNet review:
669655

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Abstract | References | Similar Articles | Additional Information

Abstract: The trajectories followed in the complex plane by all the zeros of the Hankel function and those of its derivative, when the order varies continuously along real values, are discussed.

**[1]**M. Abramowitz & I. A. Stegun (Editors),*Handbook of Mathematical Functions*, Dover, New York, 1965.**[2]**James Alan Cochran,*The zeros of Hankel functions as functions of their order*, Numer. Math.**7**(1965), 238–250. MR**0178170****[3]**Boro Döring,*Complex zeros of cylinder functions*, Math. Comp.**20**(1966), 215–222. MR**0192632**, 10.1090/S0025-5718-1966-0192632-1**[4]**A. Erdêlyi, W. Magnus, F. Oberhettinger & F. G. Tricomi,*Higher Transcendental Functions*, vol. 2, McGraw-Hill, New York, 1953, p. 62.**[5]**E. Jahnke, F. Emde & F. Lösch,*Tables of Higher Functions*, McGraw-Hill, New York, 1960. p. 229.**[6]**Yudell L. Luke,*Mathematical functions and their approximations*, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR**0501762****[7]**G. N. Watson,*A treatise on the theory of Bessel functions*, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995. Reprint of the second (1944) edition. MR**1349110**

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DOI:
https://doi.org/10.1090/S0025-5718-1982-0669655-8

Keywords:
Hankel function,
derivative of the Hankel function,
zeros

Article copyright:
© Copyright 1982
American Mathematical Society