A gamma function in two variables

[1305.2174] A gamma function in two variables Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Number Theory arXiv:1305.2174 (math) This paper has been withdrawn by Mohamed El Bachraoui [Submitted on 9 May 2013 ( v1 ), last revised 9 Apr 2026 (this version, v2)] Title: A gamma function in two variables Authors: Mohamed El Bachraoui View a PDF of the paper titled A gamma function in two variables, by Mohamed El Bachraoui No PDF available, click to view other formats Abstract: We introduce a gamma function $\Ga(x,z)$ in two complex variables which extends the classical gamma function $\Ga(z)$ in the sense that $\lim_{x\to 1}\Ga(x,z)=\Ga(z)$. We will show that many properties which $\Ga(z)$ enjoys extend in a natural way to the function $\Ga(x,z)$. Among other things we shall provide functional equations, a multiplication formula, and analogues of the Stirling formula with asymptotic estimates as consequences. Comments: Contains only well-known results Subjects: Number Theory (math.NT) MSC classes: 33B15, 11Y60, 11M06 Cite as: arXiv:1305.2174 [math.NT] (or arXiv:1305.2174v2 [math.NT] for this version) https://doi.org/10.48550/arXiv.1305.2174 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Mohamed El Bachraoui [ view email ] [v1] Thu, 9 May 2013 18:37:13 UTC (10 KB) [v2] Thu, 9 Apr 2026 09:14:55 UTC (1 KB) (withdrawn) Full-text links: Access Paper: View a PDF of the paper titled A gamma function in two variables, by Mohamed El Bachraoui Withdrawn No license for this version due to withdrawn Current browse context: math.NT < prev | next > new | recent | 2013-05 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs 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? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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