On the roots of $f_n(z)=a+K_{n+1}(z)/zK_n(z)$
Author:
R. J. Conant
Journal:
Quart. Appl. Math. 44 (1986), 425-430
MSC:
Primary 30C15; Secondary 33A40
DOI:
https://doi.org/10.1090/qam/860895
MathSciNet review:
860895
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Abstract: The function appearing in the title is examined to determine the number of roots and their general location. It is found that the roots appear in complex conjugate pairs, that the number of roots depends on $n$, and that, with the exception of a positive real root arising for $a < 0$, all roots lie in the left half-plane.
- Henrik L. Selberg, Transient compression waves from spherical and cylindrical cavities, Ark. Fys. 5 (1952), 97β108. MR 68427
- Julius Miklowitz, Plane-stress unloading waves emanating from a suddenly punched hole in a stretched elastic plate, J. Appl. Mech. 27 (1960), 165β171. MR 0110311
- M. A. Biot, Propagation of elastic waves in a cylindrical bore containing a fluid, J. Appl. Phys. 23 (1952), 997β1005. MR 69012
R. J. Conant and R. L. Mussulman, Propagation of thermoelastic surface waves in a cylindrical bore, to appear
- A. ErdΓ©lyi and W. O. Kermack, Note on the equation $f(z)Kβ_n(z)-g(z)K_n(z)=0$, Proc. Cambridge Philos. Soc. 41 (1945), 74β75. MR 11759
- G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746
H. L. Selberg, Transient compressional waves from spherical and cylindrical cavities, Arkiv FΓΆr Fysik (7) 5, 97β108 (1952)
J. Miklowitz, Plane-stress unloading waves emanating from a suddenly punched hole in a stretched elastic plate, J. Appl. Mech. 27, 165β171 (1960)
M. A. Biot, Propagation of elastic waves in a cylindrical bore containing a fluid, J. Appl. Phys. 9, 23, 997β1005 (1952)
R. J. Conant and R. L. Mussulman, Propagation of thermoelastic surface waves in a cylindrical bore, to appear
A. ErdΓ©lyi and W. O. Kermack, Note on the equation $f\left ( z \right ){Kβ_n}\left ( z \right ) - g\left ( z \right ){K_n}\left ( z \right ) = 0$, Proc. Camb. Phil. Soc. 41, 74β75 (1945)
G. N. Watson, A treatise on the theory of Bessel functions, 2nd edition, Cambridge University Press, London, p. 511 (1966)
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Article copyright:
© Copyright 1986
American Mathematical Society
