ASYMPTOTIC BOUNDS FOR ZEROS OF SPECIAL FUNCTIONS,

Abstract

Asymptotic approximations for special functions and their zeros have been used for many years in applied mathematics, often without knowledge of their accuracy. In this paper a theorem is given for finding asymptotic bounds for zeros of transcendental functions and the theorem is applied to obtain bounds on large zeros of Airy and Bessel functions. The theorem could also be applied to other Airy and Bessel functions, parabolic cylinder functions, Coulomb wave functions, and confluent hypergeometric functions. In addition to their theoretical importance, these bounds could be used to compute approximate values of large real zeros. (Author)

Document Details

Document Type
Technical Report
Publication Date
May 01, 1969
Accession Number
AD0697645

Entities

People

  • Herbert W. Hethcote

Organizations

  • University of Iowa

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Applied Mathematics
  • Bessel Functions
  • Complex Variables
  • Functions (Mathematics)
  • Hypergeometric Functions
  • Mathematical Analysis
  • Mathematics
  • Special Functions (Mathematics)
  • Transcendental Functions
  • Wave Functions

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis