Evaluation of Bessel Functions with Imaginary Order for Applications to Certain Boundary-Value Problems.
Final technical rept. 1 Jul 69-30 Jun 70,
TEXAS UNIV EL PASO
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The paper treats the mathematics of the Bessel function J sub nuz for large order and argument, resulting in the tabulation of values of the J sub nuz and J sub nx 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 Debyes asymptotic expansions. Author
- Numerical Mathematics