A double inequality for the trigamma function and its applications
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Publication:1724770
DOI10.1155/2014/702718zbMath1474.33012OpenAlexW2000707474WikidataQ59040735 ScholiaQ59040735MaRDI QIDQ1724770
Zhen-Hang Yang, Yu-Ming Chu, Xiao-Jing Tao
Publication date: 14 February 2019
Published in: Abstract and Applied Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1155/2014/702718
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Cites Work
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- Complete monotonicity of a difference between the exponential and trigamma functions and properties related to a modified Bessel function
- Moments of Ramanujan's generalized elliptic integrals and extensions of Catalan's constant
- Convex functions, partial orderings, and statistical applications
- The polygamma function \(\psi^{(k)}(x)\) for \(x={1\over 4}\) and \(x={3\over 4}\)
- COMPLETE MONOTONICITY OF A DIFFERENCE BETWEEN THE EXPONENTIAL AND TRIGAMMA FUNCTIONS
- Properties of modified Bessel functions and completely monotonic degrees of differences between exponential and trigamma functions
- Sharp bounds for the psi function and harmonic numbers
- On the rapid computation of various polylogarithmic constants
- Pi, Euler Numbers, and Asymptotic Expansions
- Some properties of the psi and polygamma functions
- A monotoneity property of the gamma function
- The best bounds in Gautschi's inequality
- Refinements of lower bounds for polygamma functions
- On proofs for monotonicity of a function involving the psi and exponential functions
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