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On the asymptotics of $ \Gamma_{q}(z)$ as $ q$ approaches $ 1$


Author: Ruiming Zhang
Journal: Proc. Amer. Math. Soc. 141 (2013), 1343-1348
MSC (2010): Primary 33D05; Secondary 33D15
Published electronically: September 4, 2012
MathSciNet review: 3008881
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Abstract: In this note we give a derivation of the asymptotic main term for the $ q$-Gamma function $ \Gamma _{q}\left (z\right )$ as $ q$ approaches $ 1$. Our formula is valid for all fixed $ z\in \mathbb{C}$ except non-positive integers.


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Additional Information

Ruiming Zhang
Affiliation: Institute of Applied Mathematics, College of Science, Northwest A&F University, Yangling, Shaanxi 712100, People’s Republic of China
Email: ruimingzhang@yahoo.com

DOI: https://doi.org/10.1090/S0002-9939-2012-11407-8
Keywords: Gamma function $Γ(z)$, $q$-Gamma function $Γ_{q}(z)$.
Received by editor(s): October 6, 2010
Received by editor(s) in revised form: August 19, 2011
Published electronically: September 4, 2012
Communicated by: Sergei K. Suslov
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.