On a transcendental equation involving quotients of Gamma functions
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- by Senping Luo, Juncheng Wei and Wenming Zou PDF
- Proc. Amer. Math. Soc. 145 (2017), 2623-2637 Request permission
Abstract:
This note is aimed at giving a complete characterization of the following equation in $p$: \[ \displaystyle p\frac {\Gamma (\frac {n}{2}-\frac {s}{p-1})\Gamma (s+\frac {s}{p-1})}{\Gamma (\frac {s}{p-1})\Gamma (\frac {n-2s}{2}-\frac {s}{p-1})} =\Big (\frac {\Gamma (\frac {n+2s}{4})}{\Gamma (\frac {n-2s}{4})}\Big )^2.\]
The method is based on some key transformations and the properties of the Gamma function. Applications to fractional nonlinear Lane-Emden equations will be given.
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Additional Information
- Senping Luo
- Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China
- Juncheng Wei
- Affiliation: Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
- MR Author ID: 339847
- ORCID: 0000-0001-5262-477X
- Wenming Zou
- Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China
- MR Author ID: 366305
- Received by editor(s): June 21, 2016
- Received by editor(s) in revised form: August 1, 2016
- Published electronically: December 15, 2016
- Additional Notes: This work was supported by NSFC of China and NSERC of Canada
- Communicated by: Mourad Ismail
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 2623-2637
- MSC (2010): Primary 33B15; Secondary 35B35
- DOI: https://doi.org/10.1090/proc/13408
- MathSciNet review: 3626516