On the roots of $f(z)=J_0(z)-iJ_1(z)$
Author:
Costas Emmanuel Synolakis
Journal:
Quart. Appl. Math. 46 (1988), 105-107
MSC:
Primary 33A40
DOI:
https://doi.org/10.1090/qam/934685
MathSciNet review:
934685
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Abstract: The function $f\left ( z \right ) = {J_0}\left ( z \right ) - i{J_1}\left ( z \right )$ is examined to determine its behavior in the complex plane. It is shown that $f\left ( z \right )$ has no zeroes in the upper half plane.
J. B. Keller and H. B. Keller, Water wave run-up on a beach, ONR Research Report Contract No. NONR-3828(00), Dept. of the Navy, Washington, DC, 40 pp. (1964)
- George F. Carrier, Gravity waves on water of variable depth, J. Fluid Mech. 24 (1966), 641–659. MR 200009, DOI https://doi.org/10.1017/S0022112066000892
C. E. Synolakis, The runup of solitary waves, J. Fluid Mech. 185, 523–545 (1987)
- G. F. Carrier and H. P. Greenspan, Water waves of finite amplitude on a sloping beach, J. Fluid Mech. 4 (1958), 97–109. MR 96462, DOI https://doi.org/10.1017/S0022112058000331
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Eighth Edition, New York; Dover Publications, 1046 pp. (1972)
J. B. Keller and H. B. Keller, Water wave run-up on a beach, ONR Research Report Contract No. NONR-3828(00), Dept. of the Navy, Washington, DC, 40 pp. (1964)
G. F. Carrier, Gravity waves of water of variable depth, J. Fluid Mech. 24, 641–659 (1966)
C. E. Synolakis, The runup of solitary waves, J. Fluid Mech. 185, 523–545 (1987)
G. F. Carrier and H. P. Greenspan, Water waves of finite amplitude on a sloping beach, J. Fluid Mech. 17, 97–110 (1958)
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Eighth Edition, New York; Dover Publications, 1046 pp. (1972)
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Article copyright:
© Copyright 1988
American Mathematical Society
