# Monotonicity Properties Related to the Ratio of Two Gamma Functions

```@article{Zhou2021MonotonicityPR,
title={Monotonicity Properties Related to the Ratio of Two Gamma Functions},
author={Nian Hong Zhou and Da-Wei Niu},
journal={Mediterranean Journal of Mathematics},
year={2021},
volume={18},
pages={1-12}
}```
• Published 5 April 2021
• Mathematics
• Mediterranean Journal of Mathematics
In this paper we investigate the monotonicity properties related to the ratio of gamma functions, from which some related asymptotics and inequalities are established. Some special cases also confirm the conjectures of C.-P. Chen (Appl Math Comput 283:385–396, 2016).

## References

SHOWING 1-10 OF 25 REFERENCES
De progressionibus transcendentibus seu quarum termini generales algebraice dari nequent
• Comm. Acad. Sci. Petr., 5:36–57,
• 1738
Arithmetica infinitorum
• Oxford,
• 1656
Error bounds for the asymptotic expansion of the ratio of two gamma functions with complex argument
Error bounds are obtained for an asymptotic expansion of the ratio of two gamma functions \${{\Gamma (z + a)} / {\Gamma (z + b)}}\$ when a and b are complex constants and \$|z|\$ is large. These bounds
Error bounds for asymptotic expansions of the ratio of two gamma functions
Error bounds are obtained for asymptotic expansions of the ratio of two gamma functions \${{\Gamma (x + a)} / {\Gamma (x + b)}}\$ for the case of real, bounded \$a,b\$ and large positive x. In particular
Monotonicity of some functions involving the gamma and psi functions
Through this result, some inequalities involving the ratio of gamma functions are obtained and some applications in the context of trigonometric sum estimation are provided.
Series Representations of the Remainders in the Expansions for Certain Functions with Applications
• Mathematics
• 2017
We present a summary of the series representations of the remainders in the expansions in ascending powers of t of \$\${2/(e^t+1)}\$\$2/(et+1), sech t and coth t and establish simple bounds for these
A Note on the Asymptotic Expansion of a Ratio of Gamma Functions
• J. Fields
• Mathematics
Proceedings of the Edinburgh Mathematical Society
• 1966
Many problems in mathematical analysis require a knowledge of the asymptotic behaviour of Γ(z + α)/Γ(z + β) for large values of |z|, where α and β are bounded quantities. Tricomi and Erdélyi in (1),