Accession Number : AD0704098

Title :   THE CONVERGING FACTOR FOR THE MODIFIED BESSEL FUNCTION OF THE SECOND KIND.

Descriptive Note : Interim rept.,

Corporate Author : NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER WASHINGTON D C

Personal Author(s) : Wrench,John W. , Jr

Report Date : JAN 1970

Pagination or Media Count : 60

Abstract : The converging factor for a specific mathematical function, such as the modified Bessel function of the second kind considered in this report, is that factor by which the last term of a truncated series (usually asymptotic) approximating the function must be multiplied to compensate for the omitted terms. This converging factor for the aforementioned Bessel function is discussed herein in detail and is shown to be related to the corresponding factor for the probability integral. Tables of this factor and its reduced derivatives, correct to 30 decimal places, are included to expedite the application of this procedure to the evaluation of this Bessel function to high precision for arguments between 5 and 20, and specific examples of such applications are presented. (Author)

Descriptors :   (*DIFFERENTIAL EQUATIONS, *NUMERICAL INTEGRATION), (*BESSEL FUNCTIONS, ASYMPTOTIC SERIES), POWER SERIES, DIFFERENCE EQUATIONS, NUMERICAL ANALYSIS, HYPERGEOMETRIC FUNCTIONS, TABLES(DATA)

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE