# 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

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### Abstract

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 .

### Journal

PositivitySpringer Journals

Published: Jun 18, 2016

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