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PreprintCC BY 4.0arXiv

The first type of power mean bounds for the Gaussian hypergeometric function

  • Zhen-Hang
  • Yang
  • Jing-Feng Tian
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Abstract

In this paper, by using a signs rule for a class of special power series and a recurrence relation of coefficients involving hypergeometric series, we find the necessary and sufficient conditions for the sharp (at the left endpoint) inequalities between the hypergeometric function and power mean (Hm-Pm inequality) to hold in all possible cases, which greatly extends those known results and solve the rest of problem on the sharp (at the left endpoint) power mean bounds for the hypergeometric mean.

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Cite

BibTeXRIS
BibTeX
@misc{zhenhang2026first,
  title = {{The first type of power mean bounds for the Gaussian hypergeometric function}},
  author = {Zhen-Hang and Yang and Jing-Feng Tian},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10581},
  eprint = {2610.10581},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10581},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The first type of power mean bounds for the Gaussian hypergeometric function
AU  - Zhen-Hang
AU  - Yang
AU  - Jing-Feng Tian
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.10581
UR  - https://arxiv.org/abs/2610.10581
AB  - In this paper, by using a signs rule for a class of special power series and a recurrence relation of coefficients involving hypergeometric series, we find the necessary and sufficient conditions for the sharp (at the left endpoint) inequalities between the hypergeometric function and power mean (Hm-Pm inequality) to hold in all possible cases, which greatly extends those known results and solve the rest of problem on the sharp (at the left endpoint) power mean bounds for the hypergeometric mean.
ER  -