Inequalities for Taylor series involving the divisor function

DOI10.21136/CMJ.2021.0464-20OpenAlexW3185935195MaRDI QIDQ5084247

Horst Alzer, Man Kam Kwong

Publication date: 23 June 2022

Published in: Czechoslovak Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.05018

zbMATH Keywords

monotonicityinfinite seriesinequalitydivisor functionEuler's constant\(q\)-digamma function

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Arithmetic functions; related numbers; inversion formulas (11A25) (q)-gamma functions, (q)-beta functions and integrals (33D05)

Cites Work

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• A completely monotonic function involving \(q\)-gamma and \(q\)-digamma functions
• Combinatorial interpretations of a recent convolution for the number of divisors of a positive integer
• An identity for the divisor generating function arising from sorting theory
• Summations for basic hypergeometric series involving a \(q\)-analogue of the digamma function
• A new look on the generating function for the number of divisors
• A certain class of approximations for the \(q\)-digamma function
• Euler's Constant, Taylor's Formula, and Slowly Converging Series
• Theq-Gamma andq-Beta Functions†
• Sharp lower and upper bounds for the q-gamma function
• Complete Monotonicity property for two functions related to the q-digamma function

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