Inequalities for the Gaussian hypergeometric function

we study the monotonicity of certain combinations of the Gaussian hypergeometric functions F(?1/2, 1/2; 1; 1 ? x ^c ) and F(?1/2 ? δ, 1/2 + δ; 1;1 ? x ^d ) on (0, 1) for given 0 < c ? 5d/6 < ∞ and δ ∈ (?1/2, 1/2), and find the largest value δ ₁ = δ ₁(c, d) such that inequality F(?1/2, 1/2; 1; 1 ? x ^c ) < F(?1/2 ? δ, 1/2 + δ; 1; 1 ? x ^d ) holds for all x ∈ (0, 1). Besides, we also consider the Gaussian hypergeometric functions F(a?1 ?δ, 1-a+δ; 1;1 ?x ³) and F(a?1, 1 ?a; 1; 1?x ²) for given a ∈ 1/29, 1) and δ ∈ (a?1, a), and obtain the analogous results.