# A class of logarithmically completely monotonic functions related to the q-gamma function and applications

A class of logarithmically completely monotonic functions related to the q-gamma function and... In this paper, the logarithmically complete monotonicity property for a functions involving q-gamma function is investigated for $$q\in (0,1).$$ q ∈ ( 0 , 1 ) . As applications of this results, some new inequalities for the q-gamma function are established. Furthermore, let the sequence $$r_n$$ r n be defined by $$n!=\sqrt{2\pi n}(n/e)^n e^{r_n}$$ n ! = 2 π n ( n / e ) n e r n . We establish new estimates for Stirling’s formula remainder $$r_n.$$ r n . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# A class of logarithmically completely monotonic functions related to the q-gamma function and applications

, Volume 21 (1) – Jun 18, 2016
13 pages

/lp/springer_journal/a-class-of-logarithmically-completely-monotonic-functions-related-to-1A8UwMYi4v
Publisher
Springer International Publishing
Copyright © 2016 by Springer International Publishing
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-016-0431-3
Publisher site
See Article on Publisher Site

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