Illinois Journal of Mathematics

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

Mourad E. H. Ismail and Plamen Simeonov

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258131107

Digital Object Identifier
doi:10.1215/ijm/1258131107

Mathematical Reviews number (MathSciNet)
MR2379727

Zentralblatt MATH identifier
1156.33002

Subjects
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]

Citation

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. https://projecteuclid.org/euclid.ijm/1258131107


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