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INEQUALITIES ASSOCIATED WITH RATIOS OF GAMMA FUNCTIONS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 97 / Issue 3 / June 2018
- Published online by Cambridge University Press:
- 23 April 2018, pp. 453-458
- Print publication:
- June 2018
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- Article
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We use properties of the gamma function to estimate the products
$\prod _{k=1}^{n}(4k-3)/4k$ and 
$\prod _{k=1}^{n}(4k-1)/4k$, motivated by the work of Chen and Qi [‘Completely monotonic function associated with the gamma function and proof of Wallis’ inequality’, Tamkang J. Math.36(4) (2005), 303–307] and Mortici et al. [‘Completely monotonic functions and inequalities associated to some ratio of gamma function’, Appl. Math. Comput.240 (2014), 168–174].
