On the roots of 𝑓(𝑧)=𝐽₀(𝑧)-𝑖𝐽₁(𝑧)-Reference-Cited by-同舟云学术

On the roots of 𝑓(𝑧)=𝐽₀(𝑧)-𝑖𝐽₁(𝑧)

Published:1988 Issue:1 Volume:46 Page:105-107
ISSN:0033-569X
Container-title:Quarterly of Applied Mathematics
language:en
Short-container-title:Quart. Appl. Math.

Author:

Synolakis Costas Emmanuel

Abstract

The function f ( z ) = J 0 ( z ) − i J 1 ( z ) 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 ( z ) f\left ( z \right ) has no zeroes in the upper half plane.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics

Link

http://www.ams.org/qam/1988-46-01/S0033-569X-1988-0934685-0/S0033-569X-1988-0934685-0.pdf

Reference5 articles.

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3. C. E. Synolakis, The runup of solitary waves, J. Fluid Mech. 185, 523–545 (1987)

4. Water waves of finite amplitude on a sloping beach;Carrier, G. F.;J. Fluid Mech.,1958

5. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Eighth Edition, New York; Dover Publications, 1046 pp. (1972)

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