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Zeros of Bessel Functions and Eigenvalues of Non-self-adjoint Boundary Value Problems

Cohen, Donald S. (1964) Zeros of Bessel Functions and Eigenvalues of Non-self-adjoint Boundary Value Problems. Journal of Mathematics and Physics, 43 (1-4). pp. 133-139. ISSN 0097-1421.

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For many non-self-adjoint boundary value problems involving the wave equation and the reduced wave equation in domains exterior to cylinders and spheres, it has recently been shown [1]-[5] that new representations of the solutions may be found systematically. In modern applications (e.g., potential scattering and diffraction phenomena) those alternative representations are usually more rapidly convergent than the classical ones, and asymptotic expansions with respect to parameters can often be found from them. These investigations require extensive knowledge of the zeros of certain linear combinations of the Hankel function and its first derivative considered as functions of the order of the Hankel function (with fixed argument). The most complete studies of these zeros are those of Magnus and Kotin [6] and Keller, Rubinow, and Goldstein [7]. The latter paper stressed their importance as poles of scattering amplitudes.

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Additional Information:© 1964 by the Massachusetts Institute of Technology. Manuscript received: 15 November 1963. This research was begun while the author was at the Courant Institute of Mathematical Sciences. It was completed at Rensselaer Polytechnic Institute where it was supported by the Air Office of Scientific Research under Contract Number AF-AFOSR-182-63.
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Air Force Office of Scientific Research (AFOSR)AF-AFOSR-182-63
Issue or Number:1-4
Record Number:CaltechAUTHORS:20200115-074727243
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Official Citation:Cohen, Donald S, (1964), Zeros of Bessel Functions and Eigenvalues of Non‐self‐adjoint Boundary Value Problems, Journal of Mathematics and Physics, 43, doi: 10.1002/sapm1964431133.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100726
Deposited By: Tony Diaz
Deposited On:15 Jan 2020 18:20
Last Modified:15 Jan 2020 18:20

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