Inequalities for generalized hypergeometric functions of three variables

Abstract

LUKE (5] has developed a technique of obtaining two-sided inequalities for generalized hypergeometric functions through their Eulerian integral-representations. We exploit the technique suggested by him in obtaining inequalities for Lauricella funtions Fa,FB and FD. Specific numerics have been given in support of the algebra involved and to lend credence to the validity of various formulas that are presented. The bounds obtained are worth while since evaluation of inequalities often takes much less effort than evaluation of a triple series. In the sequel, corrections in theorems 2 and 6 of Luke (5) are also presented.

Keywords

• generalized hypergeometric functions
• appell functions
• lauricella functions