Accession Number : AD0706390

Title :   INEQUALITIES FOR GENERALIZED HYPERGEOMETRIC FUNCTIONS,

Corporate Author : MIDWEST RESEARCH INST KANSAS CITY MO

Personal Author(s) : Luke,Yudell L.

Report Date : MAR 1970

Pagination or Media Count : 40

Abstract : It is shown that some well-known Pade approximations for a particular form of the Gaussian hypergeometric function and two of its confluent forms give upper and lower bounds for these functions under suitable restrictions on the parameters and variable. With the aid of the beta and Laplace transforms, two-sided inequalities are derived for the pFq generalized hypergeometric function, p = q or p = q + 1, and for a particular form of Meijer's G-function. Several examples are developed. These include upper and lower bounds for certain elementary functions, complete elliptic integrals, the incomplete gamma function, modified Bessel functions and parabolic cylinder functions. (Author)

Descriptors :   (*HYPERGEOMETRIC FUNCTIONS, INEQUALITIES), BESSEL FUNCTIONS, MEROMORPHIC FUNCTIONS, INTEGRAL TRANSFORMS, NUMERICAL ANALYSIS, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE