Monotonic functions related to the $q$-gamma and q-trigamma functions with applications
نویسندگان
چکیده
منابع مشابه
COMPLETELY MONOTONIC FUNCTIONS INVOLVING THE GAMMA AND q-GAMMA FUNCTIONS
We give an infinite family of functions involving the gamma function whose logarithmic derivatives are completely monotonic. Each such function gives rise to an infinitely divisible probability distribution. Other similar results are also obtained for specific combinations of the gamma and q-gamma functions.
متن کاملA COMPLETELY MONOTONIC FUNCTION RELATING TO THE q –TRIGAMMA FUNCTION
In the paper, a function relating to the q -trigamma function is proved to be completely monotonic. As by-products, two functions relating to the logarithmic function are also proved to be completely monotonic. Mathematics subject classification (2010): Primary 33D05; Secondary 26A48.
متن کاملCERTAIN LOGARITHMICALLY N-ALTERNATING MONOTONIC FUNCTIONS INVOLVING GAMMA AND q-GAMMA FUNCTIONS
In the paper, three basic properties of the logarithmically N alternating monotonic functions are established and the monotonicity results of some functions involving the gamma and q-gamma functions, which are obtained in [W. E. Clark and M. E. H. Ismail, Inequalities involving gamma and psi functions, Anal. Appl. (Singap.) 1 (2003), no. 1, 129–140.], are generalized to the logarithmically N -a...
متن کاملTHE MULTIPLE GAMMA FUNCTIONS AND THE MULTIPLE q-GAMMA FUNCTIONS
We give an asymptotic expansion (the higher Stirling formula) and an infinite product representation (the Weierstrass product representation) of the Vignéras multiple gamma functions by considering the classical limit of the multiple q-gamma functions.
متن کاملSome inequalities for the q-beta and the q-gamma functions via some q-integral inequalities
Some new inequalities for the q-gamma, the q-beta and the q-analogue of the Psi functions are established via some q-integral inequalities. In classical analysis, integral inequalities have been well-developed and leading to a wide variety of applications in mathematics and physics (see [11–13] and references therein). In a survey paper [4], Dragomir et al. used certain clever integral inequali...
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ژورنال
عنوان ژورنال: Journal of Classical Analysis
سال: 2017
ISSN: 1848-5987
DOI: 10.7153/jca-10-14