Sharp bounds for a ratio of the q-gamma function in terms of the q-digamma function

Abstract

Abstract In the present paper, we introduce sharp upper and lower bounds to the ratio of two q-gamma functions Γ q ( x + 1 ) / Γ q ( x + s ) ${\Gamma }_{q}(x+1)/{\Gamma }_{q}(x+s)$ for all real number s and 0 1 $s>1$ .

Keywords

• q-Gamma function
• q-Digamma function
• Inequalities
• Completely monotonic function