Sharp Smith’s bounds for the gamma function

Among various approximation formulas for the gamma function, Smith showed that [Formula: see text] which is a little-known but accurate and simple one. In this note, we prove that the function [Formula: see text] is strictly increasing and concave on [Formula: see text] , which shows that Smith’s ap...

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Detalles Bibliográficos
Autores principales: Li, Xi-Qiao, Liu, Zhi-Ming, Yang, Zhen-Hang, Zheng, Shen-Zhou
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5846881/
https://www.ncbi.nlm.nih.gov/pubmed/29568209
http://dx.doi.org/10.1186/s13660-018-1620-3
Descripción
Sumario:Among various approximation formulas for the gamma function, Smith showed that [Formula: see text] which is a little-known but accurate and simple one. In this note, we prove that the function [Formula: see text] is strictly increasing and concave on [Formula: see text] , which shows that Smith’s approximation is just an upper one.

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