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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Bernoulli inequality and hypergeometric functions


Authors: Riku Klén, Vesna Manojlović, Slavko Simić and Matti Vuorinen
Journal: Proc. Amer. Math. Soc. 142 (2014), 559-573
MSC (2010): Primary 26D07, 33C05
Published electronically: October 25, 2013
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Abstract: Bernoulli type inequalities for functions of logarithmic type are given. These functions include, in particular, Gaussian hypergeometric functions in the zero-balanced case $ F(a,b;a+b;x).$


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Additional Information

Riku Klén
Affiliation: Department of Mathematics and Statistics, University of Turku, 20014 Turku, Finland
Email: ripekl@utu.fi

Vesna Manojlović
Affiliation: Faculty of Organizational Sciences, University of Belgrade, Jove Ilica 154, 11000 Belgrade, Serbia
Email: vesnam@fon.rs

Slavko Simić
Affiliation: Mathematical Institute SANU, Kneza Mihaila 36, 11000 Belgrade, Serbia
Email: ssimic@turing.mi.sanu.ac.rs

Matti Vuorinen
Affiliation: Department of Mathematics and Statistics, University of Turku, 20014 Turku, Finland
Email: vuorinen@utu.fi

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11781-8
PII: S 0002-9939(2013)11781-8
Keywords: Log-convexity, hypergeometric functions, inequalities
Received by editor(s): July 21, 2011
Received by editor(s) in revised form: March 20, 2012
Published electronically: October 25, 2013
Additional Notes: The fourth author was supported by the Academy of Finland, project 2600066611
Communicated by: Walter Van Assche
Article copyright: © Copyright 2013 American Mathematical Society