A class of two-sided inequalities involving the psi and polygamma functions

DOI10.1080/10652460903403596zbMath1200.33003OpenAlexW1975885680MaRDI QIDQ3584667

Chao-Ping Chen, Hari M. Srivastava

Publication date: 30 August 2010

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652460903403596

zbMATH Keywords

gamma functionRiemann zeta functioninequalitiesEuler-Mascheroni constantpsi functionpolygamma functionstwo-sided inequalitiesHurwitz (or generalized) zeta functionweighted arithmetic-geometric inequality

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Gamma, beta and polygamma functions (33B15) Convexity of real functions in one variable, generalizations (26A51) Monotonic functions, generalizations (26A48) Hurwitz and Lerch zeta functions (11M35) Inequalities involving other types of functions (26D07)

Related Items (6)

Complete characterizations of the gamma function ⋮ Solvability of some nonlocal boundary value problems for the Helmholtz equation in a half-disk ⋮ Monotonicity properties of functions related to the psi function ⋮ Estimating the digamma and trigamma functions by completely monotonicity arguments ⋮ Inequalities associated with Čebyšev functional for Saigo fractional integration operator ⋮ Inequalities and monotonicity properties for the psi (or digamma) function and estimates for the Euler–Mascheroni constant

Cites Work

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• A remark on a class of double inequalities of Batir
• Remarks on some series expansions associated with certain products of the incomplete Gamma functions
• Some expansions of the exponential integral in series of the incomplete Gamma function
• Integral representations for the Gamma function, the Beta function, and the Double Gamma function
• Logarithmically completely monotonic functions concerning gamma and digamma functions
• Three classes of logarithmically completely monotonic functions involving gamma and psi functions
• Two logarithmically completely monotonic functions connected with gamma function

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