Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Number Theory

arXiv:1805.01999 (math)
[Submitted on 5 May 2018 (v1), last revised 24 Feb 2019 (this version, v2)]

Title:Some new inequalities for the $q$-gamma and related functions

Authors:Mohamed El Bachraoui, József Sándor
View PDF
Abstract:We consider convexity and monotonicity properties for some functions related to the $q$-gamma function. As applications, we give a variety of inequalities for the $q$-gamma function, the $q$-digamma function $\psi_q(x)$, and the $q$-series. Among other consequences, we improve a result of Azler~and~Grinshpan about the zeros of the function $\psi_q(x)$.
We use $q$-analogues for the Gauss multiplication formula to put in closed form members of some of our inequalities.
Comments: Submitted 23 January 2019, pages 17
Subjects: Number Theory (math.NT)
MSC classes: 33B15, 26D15, 33E05
Cite as: arXiv:1805.01999 [math.NT]
  (or arXiv:1805.01999v2 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1805.01999

Submission history

From: Mohamed El Bachraoui [view email]
[v1] Sat, 5 May 2018 04:59:32 UTC (12 KB)
[v2] Sun, 24 Feb 2019 10:06:51 UTC (13 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.NT
< prev   |   next >
new | recent | 2018-05
Change to browse by:
math

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)