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Complete monotonicity properties of functions involving the Gamma function and their q-analogues(PDF)

《纺织高校基础科学学报》[ISSN:1006-6977/CN:61-1281/TN]

Issue:
2016年03期
Page:
299-305
Research Field:
Publishing date:

Info

Title:
Complete monotonicity properties of functions involving the Gamma function and their q-analogues
Author(s):
 LI JingjingSUN Mei
 Department of Mathematics, Northwest University, Xi’an 710127, China
Keywords:
 complete monotonicity Gamma function <i>q</i>-analogue function sufficient condition
PACS:
O 174.6
DOI:
10.13338/j.issn.1006-8341.2016.03.005
Abstract:
A investigation to derive the complete monotonicities of functions involving the Gamma function and their q-analogues is presented. First of all, using the integral representations and the monotonicity theory,it is proved that the complete monotonicities of functions Fα(x)=ψ’(x)+α/x-1/(x+1), fα(x)=lnx-ψ(x)-α/x and f(x)=lnx-ψ(x)+1/x22 on(0,∞); Second, based on the properties of q-analogues, the complete monotonicities of q-analogues about these three functions are respectively discussed by the series expansion of functions, the monotonicity theory and induction, and two inequalities are obtained because of the property.

References:

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Last Update: 2016-10-08