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Inequalities and monotonicity properties for the gamma function. (English) Zbl 0985.33003
After an extensive survey of previous results by the authors and others, they offer the inequalities \[ \Gamma[1+x+(1/x)]/2\leq \Gamma(1+x)\Gamma[1+(1/x)]<\Gamma[1+x+(1/x)] \] \((x>0; \) equality on the left at \(x=1\)), counter examples to the left inequality for more terms and factors, and proof of a weakened form of that generalization.

MSC:
33B15 Gamma, beta and polygamma functions
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