Evaluation of Bessel Functions with Imaginary Order for Applications to Certain Boundary-Value Problems.
Abstract
The paper treats the mathematics of the Bessel function (J sub nu)(z) for large order and argument, resulting in the tabulation of values of the (J sub nu)(z) and (J sub n)(x) functions for pure imaginary order nu = in and complex argument z, and for real order n and real argument x, for n = 100, 1000, 10000, and 100000. Heretofore, tables of imaginary order were not available in the literature, and have now been computed in this work for the purpose of applying them to the theory of sound propagation in a medium where the conditions are such as to produce shadow zones. Of particular interest are future applications to the yet unsolved problem of computing mathematically the intensity of sound in the atmospheric shadow zone in terms of wind gradients. The Bessel function evaluations are based on Debye's asymptotic expansions. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1970
- Accession Number
- AD0728833
Entities
People
- Phillip H. Duran
Organizations
- University of Texas at El Paso