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Sharp bounds for a ratio of the q-gamma function in terms of the q-digamma function.
- Source :
-
Journal of Inequalities & Applications . 6/12/2021, Vol. 2021 Issue 1, p1-12. 12p. - Publication Year :
- 2021
-
Abstract
- In the present paper, we introduce sharp upper and lower bounds to the ratio of two q-gamma functions Γ q (x + 1) / Γ q (x + s) for all real number s and 0 < q ≠ 1 in terms of the q-digamma function. Our results refine the results of Ismail and Muldoon (Internat. Ser. Numer. Math., vol. 119, pp. 309–323, 1994) and give the answer to the open problem posed by Alzer (Math. Nachr. 222(1):5–14, 2001). Also, for the classical gamma function, our results give a Kershaw inequality for all 0 < s < 1 when letting q → 1 and a new inequality for all s > 1 . [ABSTRACT FROM AUTHOR]
- Subjects :
- *GAMMA functions
*REAL numbers
*MONOTONIC functions
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 10255834
- Volume :
- 2021
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Inequalities & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 150893254
- Full Text :
- https://doi.org/10.1186/s13660-021-02642-7