Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] Henrik L. Selberg, Transient compression waves from spherical and cylindrical cavities, Ark. Fys. 5 (1952), 97–108. MR 0068427
  • [2] Julius Miklowitz, Plane-stress unloading waves emanating from a suddenly punched hole in a stretched elastic plate, J. Appl. Mech. 27 (1960), 165–171. MR 0110311
  • [3] M. A. Biot, Propagation of elastic waves in a cylindrical bore containing a fluid, J. Appl. Phys. 23 (1952), 997–1005. MR 0069012
  • [4] R. J. Conant and R. L. Mussulman, Propagation of thermoelastic surface waves in a cylindrical bore, to appear
  • [5] A. Erdélyi and W. O. Kermack, Note on the equation 𝑓(𝑧)𝐾’_{𝑛}(𝑧)-𝑔(𝑧)𝐾_{𝑛}(𝑧)=0, Proc. Cambridge Philos. Soc. 41 (1945), 74–75. MR 0011759
  • [6] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 30C15, 33A40

Retrieve articles in all journals with MSC: 30C15, 33A40

Additional Information

DOI: https://doi.org/10.1090/qam/860895
Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society