Accession Number : AD0697645

Title :   ASYMPTOTIC BOUNDS FOR ZEROS OF SPECIAL FUNCTIONS,

Corporate Author : IOWA UNIV IOWA CITY

Personal Author(s) : Hethcote,Herbert W.

Report Date : MAY 1969

Pagination or Media Count : 6

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)

Descriptors :   (*BESSEL FUNCTIONS, ASYMPTOTIC SERIES), APPROXIMATION(MATHEMATICS), HYPERGEOMETRIC FUNCTIONS, WAVE FUNCTIONS, DIFFERENTIAL EQUATIONS, INEQUALITIES, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE