Inequalities for the gamma function

Author:
Horst Alzer

Journal:
Proc. Amer. Math. Soc. **128** (2000), 141-147

MSC (1991):
Primary 33B15; Secondary 26D07

DOI:
https://doi.org/10.1090/S0002-9939-99-04993-X

Published electronically:
June 30, 1999

MathSciNet review:
1622757

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove the following two theorems:

(i) Let be the th power mean of and . The inequality

holds for all if and only if , where denotes Euler's constant. This refines results established by W. Gautschi (1974) and the author (1997).

(ii) The inequalities

are valid for all if and only if and , while holds for all if and only if and . These bounds for improve those given by G. D. Anderson an S.-L. Qiu (1997).

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Additional Information

**Horst Alzer**

Affiliation:
Morsbacher Str. 10, 51545 Waldbröl, Germany

DOI:
https://doi.org/10.1090/S0002-9939-99-04993-X

Keywords:
Gamma function,
psi function,
power mean,
inequalities

Received by editor(s):
March 10, 1998

Published electronically:
June 30, 1999

Communicated by:
Hal L. Smith

Article copyright:
© Copyright 1999
American Mathematical Society