Precise estimates for differences of the Gaussian hypergeometric function

[摘要] By showing certain combinations of the Gaussian hypergeometric functions F(a, b; a + b; 1 - x(c)) and F(a - delta, b + delta; a + b; 1 - x(d)) to be monotone on (0, 1) for given a, b, c, d is an element of (0,infinity), a less than or equal to b, and c < d, the authors study the problem of comparing these two functions. They find sup{delta is an element of (0, a): F(a, b; a + b; 1 - x(c)) < F(a - delta, b + delta; a + b; 1 - x(d)) for x is an element of (0, 1)}, thus solving an open problem and a recent conjecture. (C) 1997 Academic Press.

[发布日期] 1997-11-01