Some exact constants for the approximation of the quantity in the Wallis' formula
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Publication:395781
DOI10.1186/1029-242X-2013-67zbMath1281.41010WikidataQ59301877 ScholiaQ59301877MaRDI QIDQ395781
Jian-Guo Xu, Feng Qi, Sen-Lin Guo
Publication date: 30 January 2014
Published in: Journal of Inequalities and Applications (Search for Journal in Brave)
Gamma, beta and polygamma functions (33B15) Other analytical inequalities (26D20) Best constants in approximation theory (41A44)
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Cites Work
- Some properties of a class of functions related to completely monotonic functions
- A conjecture concerning a completely monotonic function
- Complete monotonicity results for some functions involving the gamma and polygamma functions
- A certain function class related to the class of logarithmically completely monotonic functions
- Complete monotonicity of some functions involving polygamma functions
- A class of logarithmically completely monotonic functions and application to the best bounds in the second Gautschi-Kershaw's inequality
- A class of logarithmically completely monotonic functions
- Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function
- Necessary and sufficient conditions for functions involving the tri- and tetra-gamma functions to be completely monotonic
- Wendel's and Gautschi's inequalities: refinements, extensions, and a class of logarithmically completely monotonic functions
- On some properties of the gamma function
- Some properties of completely monotonic sequences and related interpolation
- A class of logarithmically completely monotonic functions and the best bounds in the second Kershaw's double inequality
- Monotonicity properties of the gamma function
- Supplements to a class of logarithmically completely monotonic functions associated with the gamma function
- Logarithmically completely monotonic functions relating to the gamma function
- A class of logarithmically completely monotonic functions associated with the gamma function
- Some completely monotonic functions involving polygamma functions and an application
- SOME LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTIONS RELATED TO THE GAMMA FUNCTION
- A class of logarithmically completely monotonic functions related to the gamma function with applications
- Completely monotonic functions involving the gamma and $q$-gamma functions
- The best bounds in Wallis’ inequality
- Three classes of logarithmically completely monotonic functions involving gamma and psi functions
- Necessary and sufficient conditions for two classes of functions to be logarithmically completely monotonic
- Some completely monotonic functions involving the gamma and polygamma functions
