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A functional inequality for the polygamma functions

Published online by Cambridge University Press:  17 April 2009

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

where ψ denotes the logarithmic derivative of Euler's gamma function. We prove that the functional inequality

holds if and only if 0 < r ≤ 1. And, we show that the converse is valid if and only if r < 0 or r ≥ n + 1.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 72 , Issue 3 , December 2005 , pp. 455 - 459
Copyright
Copyright © Australian Mathematical Society 2005

References

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