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Inequalities for ratios of Gamma functions
Abstract
We prove that the function log (Γ(x+a+b)Γ(x))/(Γ(x+a)Γ(x+b))−blog(1+a/x) is a generalized Stieltjes function of order $3$ for a>0 and 0<b<1. A similar result is obtained when a>0 and b>1.
Related
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BibTeX
@misc{pedersen2026inequalities,
title = {{Inequalities for ratios of Gamma functions}},
author = {Henrik Laurberg Pedersen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28523},
eprint = {2609.28523},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28523},
}
RIS
TY - UNPB
TI - Inequalities for ratios of Gamma functions
AU - Henrik Laurberg Pedersen
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.28523
UR - https://arxiv.org/abs/2609.28523
AB - We prove that the function log (Γ(x+a+b)Γ(x))/(Γ(x+a)Γ(x+b))−blog(1+a/x) is a generalized Stieltjes function of order $3$ for a>0 and 0<b<1. A similar result is obtained when a>0 and b>1.
ER -