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Zbl 0536.33002
Kershaw, D.
Some extensions of W. Gautschi's inequalities for the gamma function. (English)
[J] Math. Comput. 41, 607-611 (1983). ISSN 0025-5718; ISSN 1088-6842

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.
[M.E.Muldoon]

MSC 2000:: *33B15 Gamma-functions, etc.
26D20 Analytical inequalities involving real functions

Keywords: gamma function; inequalities

Cited in: Zbl 1045.33004 Zbl 1160.33301 Zbl 0677.33001

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