Illinois Journal of Mathematics

Inequalities and asymptotics for a terminating ${}\sb 4F\sb 3$ series

Mourad E. H. Ismail and Plamen Simeonov

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In this paper we give upper bounds for a certain terminating ${}_4F_3$ series. Our estimates confirm special cases of a conjecture of Kresch and Tamvakis. We also give asymptotic estimates when the parameters in the ${}_4F_3$ series are large, and they confirm the same conjecture.

Article information

Illinois J. Math., Volume 51, Number 3 (2007), 861-881.

First available in Project Euclid: 13 November 2009

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Zentralblatt MATH identifier

Primary: 33C20: Generalized hypergeometric series, $_pF_q$
Secondary: 26D15: Inequalities for sums, series and integrals 30E15: Asymptotic representations in the complex domain 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions]


Ismail, Mourad E. H.; Simeonov, Plamen. Inequalities and asymptotics for a terminating ${}\sb 4F\sb 3$ series. Illinois J. Math. 51 (2007), no. 3, 861--881. doi:10.1215/ijm/1258131107.

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