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Generalized hypergeometric functions: product identities and weighted norm inequalities

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Abstract

We describe a method of obtaining weighted norm inequalities for generalized hypergeometric functions. This method is based upon our recent convolution theorem and some classical hypergeometric identities. In particular, it is shown that some product identities involving the divergent hypergeometric series lead to the convergent hypergeometric inequalities. A number of the new weighted norm inequalities for the Gaussian hypergeometric function, confluent hypergeometric function, and other generalized hypergeometric functions are presented.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of South Florida, Tampa, Fl, 33620, USA

    Arcadii Z. Grinshpan

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  1. Arcadii Z. Grinshpan
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Correspondence to Arcadii Z. Grinshpan.

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Dedicated to Mourad Ismail and Dennis Stanton

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Grinshpan, A.Z. Generalized hypergeometric functions: product identities and weighted norm inequalities. Ramanujan J 31, 53–66 (2013). https://doi.org/10.1007/s11139-013-9487-x

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  • DOI: https://doi.org/10.1007/s11139-013-9487-x

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