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

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

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]**J. A. Cochran, "The zeros of Hankel functions as functions of their order,"*Numer. Math.*, v. 7, 1965, pp. 238-250. MR**0178170 (31:2428)****[3]**B. Döring, "Complex zeros of cylinder functions,"*Math. Comp.*, v. 20, 1966, pp. 215-222. MR**0192632 (33:857)****[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]**Y. L. Luke,*Mathematical Functions and their Approximations*, Academic Press, New York, 1975. MR**0501762 (58:19039)****[7]**G. N. Watson,*A Treatise on the Theory of Bessel Functions*, 2nd ed., Cambridge Univ. Press, New York, 1958, Chapter XV. MR**1349110 (96i:33010)**

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Additional Information

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