Author:
Sitnik Sergei M.,Mehrez Khaled
Abstract
AbstractIn 1993 one of the authors formulated some conjectures on monotonicity of ratios for exponential series sections. These lead to a more general conjecture on monotonicity of ratios of Kummer hypergeometric functions, which remained open ever since. In this paper we prove some conjectures for Kummer hypergeometric functions and its further generalizations for Gauss and generalized hypergeometric functions. The results are also closely connected with Turán-type inequalities.
Subject
Applied Mathematics,Numerical Analysis,Analysis
Reference50 articles.
1. On the monotonicity of certain functionals in the theory of analytic functions;Ann. Univ. M. Curie-Skłodowska,1995
2. Series expansions for the third incomplete elliptic integral via partial fraction decompositions;J. Comput. Appl. Math.,2007
3. On the Riesz constants for systems of integer translates.;Math. Notes,2014
4. unpublished preprint;Sitnik,1994
5. Log-convexity and log-concavity for series in gamma ratios and applications;J. Math. Anal. Appl.,2013
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