Sharp Bounds for the Ratio ofq - Gamma Functions

Let Γq (0 < q ≠ 1) be the q–gamma function and let s ∈ (0, 1) be a real number. We determine the largest number α = α(q, s) and the smallest number β = β(q, s) such that the inequalities hold for all positive real numbers x. Our result refines and extends recently published inequalities by Ismail and Muldoon (1994).

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