Turán’s inequality for the Kummer function of the phase shift of two parameters


Direct and inverse Turán’s inequalities are proved for the confluent hypergeometric function (the Kummer function) viewed as a function of the phase shift of the upper and lower parameters. The inverse Turán inequality is derived from a stronger result on the log-convexity of a function of sufficiently general form, a particular case of which is the Kummer function. Two conjectures on the log-concavity of the Kummer function are formulated. The paper continues the previous research on the log-convexity and log-concavity of hypergeometric functions of parameters conducted by a number of authors. Bibliography: 18 titles.


Russia Phase Shift Apply Mathematic Hypergeometric Function Strong Result 
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© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of SciencesVladivostockRussia

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