Bounds for \(q\)-integrals of \({}_{r+1}\psi_{r+1}\) with applications

DOI10.1186/s13660-015-0946-3zbMath1333.33023OpenAlexW2217879401WikidataQ59434019 ScholiaQ59434019MaRDI QIDQ903382

Zhefei He, Mingjin Wang, Gaowen Xi

Publication date: 5 January 2016

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-015-0946-3

zbMATH Keywords

convergenceinequality\(q\)-integralthe bilateral basic hypergeometric function \({}_{r+1}\psi_{r+1}\)

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Inequalities for sums, series and integrals (26D15)

Cites Work

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• Unified treatment of Gautchi-Kershaw type inequalities for the gamma function
• Convergence and asymptotic behavior of Jackson integrals associated with irreducible reduced root systems.
• On the Bernstein-type inequalities for ultraspherical polynomials
• Supplements to known inequalities for some special functions
• Quantum integral inequalities on finite intervals
• On a \(q\)-analog of some numbers and polynomials
• Approximation properties of bivariate extension of \(q\)-Szász-Mirakjan-Kantorovich operators
• Inequalities for Zero-Balanced Hypergeometric Functions
• A New Family of q-analogue of Genocchi Numbers and Polynomials of Higher Order
• Some convergence theorems for the $q$-integral
• Inequalities and monotonicity properties for the gamma function

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