The Converging Factor for the Modified Bessel Function of The Second Kind

摘要

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)