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Monotonicity and concavity properties of the Gaussian hypergeometric functions, with applications (Journal Article)

By: Contributor(s): Material type: TextTextSeries: Indian Journal of Pure and Applied Mathematics ; , Volume 54: Number 4, December 2023Publication details: New Delhi :Indian National Science Academy | Springer ,2023Description: 1105-1124pISSN:
  • 0019-5588
Subject(s): Online resources:
Contents:
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Summary: Abstract: This paper deals with the monotonicity and concavity properties of certain functions involving the Gaussian hypergeometric function. With these results, we not only obtain sharp bounds for the ratio of hypergeometric functions which extend recently discovered inequalities for k-balanced hypergeometric functions, and but also give an affirmative answer to an open problem proposed by Qiu and Vuorinen. In addition, as by-products, some monotonicity theorems for complete p-elliptic integrals and inequalities for generalized Grötzsch ring function are established.
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***______{For Hard Copy, Please visit Library.}________***

Abstract: This paper deals with the monotonicity and concavity properties of certain functions involving the Gaussian hypergeometric function. With these results, we not only obtain sharp bounds for the ratio of hypergeometric functions which extend recently discovered inequalities for k-balanced hypergeometric functions, and but also give an affirmative answer to an open problem proposed by Qiu and Vuorinen. In addition, as by-products, some monotonicity theorems for complete p-elliptic integrals and inequalities for generalized Grötzsch ring function are established.

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