Inequalities for generalized hypergeometric functions

AbstractIt is shown that some well-known Padé 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 generalized hypergeometric function pFq, 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