INEQUALITIES FOR GENERALIZED HYPERGEOMETRIC FUNCTIONS,

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)

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1970
Accession Number
AD0706390

Entities

People

  • Yudell L. Luke

Organizations

  • MRIGlobal

Tags

DTIC Thesaurus Topics

  • Bessel Functions
  • Complex Variables
  • Functions (Mathematics)
  • Hypergeometric Functions
  • Inequalities
  • Integrals
  • Mathematical Analysis

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Linear Algebra