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

Tags

DTIC Thesaurus Topics

  • Asymptotic Series
  • Bessel Functions
  • Boundaries
  • Boundary Value Problems
  • Intensity
  • Literature
  • Mathematical Analysis
  • Mathematics
  • Test And Evaluation

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Linear Algebra
  • Theoretical Analysis.