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Some extensions of W. Gautschi’s inequalities for the gamma function. (English) Zbl 0536.33002
The author provides the two lower bounds $[x+s/2]\sp{1-s},\quad \exp [(1- s)\psi(x+s\sp{\frac{1}{2}})]$ and the two upper bounds $[x- frac{1}{2}+(s+1/4)\sp{\frac{1}{2}}]\sp{1-s}.\quad \exp [(1- s)\psi(x+(s+1)/2)]$ for the ratio $\Gamma(x+1)/\Gamma(x+s),\quad x>0,\quad 0<s<1.$ These results are compared with each other as well as with earlier bounds due, separately, to W. Gautschi, to T. Erber and to J. D. Kečkić and P. M. Vasić. The present bounds are generally sharper than the earlier ones but the discussion is marred by references to formulas ”(3.7)” and ”(3.8)” which do not appear in the text.
Reviewer: M.E.Muldoon

33B15Gamma, beta and polygamma functions
26D20Analytical inequalities involving real functions
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