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Inequalities for the beta function of n variables

Published online by Cambridge University Press:  17 February 2009

Horst Alzer
Horst Alzer
Affiliation:
Morsbacher Str. 10, 51545 Waldbröl, Germany; e-mail: alzerhorst@freenet.de.
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Abstract

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We present various inequalities for Euler's beta function of n variables. One of our theorems states that the inequalities

hold for all xi ≥ (i = 1,… n; n ≥ 3) with the best possible constants an = 0 and bn = 1 − 1/(n − 1)!. This extends a recently published result of Dragomir et al., who investigated (*) for the special case n = 2.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 4 , April 2003, pp. 609 - 623
Copyright
Copyright © Australian Mathematical Society 2003

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