Proofs of some conjectures on monotonicity of ratios of Kummer, Gauss and generalized hypergeometric functions

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Inequalities for sections of exponential function series and proofs of some conjectures on monotonicity of ratios of Kummer, Gauss and generalized hypergeometric functions

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Inequalities and monotonicity of ratios for generalized hypergeometric function

Abstract. We find two-sided inequalities for the generalized hypergeometric function with positive parameters restricted by certain additional conditions. Our lower bounds are asymptotically precise at x = 0, while the upper bounds are either asymptotically precise or at least agree with q+1Fq((aq+1), (bq);−x) at x = ∞. Inequalities are derived as corollaries of a theorem asserting the monotony...

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ژورنال

عنوان ژورنال: Analysis

سال: 2016

ISSN: 0174-4747,2196-6753

DOI: 10.1515/anly-2015-0029