2000 IEEE.
Personal use of this material is
permitted. However, permission to reprint/republish this
material for advertising or promotional purposes or for
creating new collective works for resale or redistribution
to servers or lists, or to reuse any copyrighted component
of this work in other works must be obtained from the
IEEE.
IEEE Transactions on Antennas and Propagation
Volume 48 Number 10, October 2000
Table of Contents for this issue
Complete paper in PDF format
An Accurate Closed-Form Approximate
Representation for the Hankel Function of the Second Kind
Judd Gardner and R. E. Collin
Page 1699.
Abstract:
A second-order asymptotic evaluation of the Hankel function is
presented and its numerical evaluation for the case of large orders and large
arguments is compared with the numerical results obtained using forward recursion.
It is shown that the second-order results are very accurate as long as the
argument is a few percent larger than the order of the function.
References
-
J. Wait,
Electromagnetic Radiation from Cylindrical Structures, New York:
Pergamon, 1959, p. 63.
-
J. Gardner, "Scattering of a Gaussian beam by a large perfectly conducting cylinder with
application to optical sensors", Ph.D. dissertation, Case Western Reserve Univ., Cleveland,
OH, 1999.
-
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, New York: Academic, 1965.
-
G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge: U.K.:
Cambridge Univ. Press, 1958.
-
A. Sommerfeld, Partial Differential Equations in Physics, New York: Academic, 1949.
-
R. Wong,
Asymptotic Approximations of Integrals, New York: Academic, 1989.