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Some beta-function inequalities

Published online by Cambridge University Press:  12 July 2007

Horst Alzer
Horst Alzer
Affiliation:
Morsbacher Str. 10, D-51545 Waldbröl, Germany ([email protected])
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Abstract

We present several new inequalities for Euler's beta function, B(x, y). One of our results states that the beta function can be approximated on (0, 1] × (0, 1] by rational functions as follows, with the best possible constants α = 1 and β = ⅔π2 − 4 = 2.579 73 ….

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 4 , August 2003 , pp. 731 - 745
Copyright
Copyright © Royal Society of Edinburgh 2003

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