Turán’s inequality for the Kummer function of the phase shift of two parameters |
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Authors: | D B Karp |
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Institution: | (1) Trent University, Peterborough, Ontario K9J 7B8, Canada;(2) University of California at Irvine, Irvine, CA 92697, USA |
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Abstract: | 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. |
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Keywords: | |
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