Inequalities for the gamma and q-gamma functions
نویسندگان
چکیده
منابع مشابه
Some 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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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.
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We present new inequalities for the gamma and psi functions, and we provide new classes of completely monotonic, star-shaped, and superadditive functions which are related to Γ and ψ. 1 Euler’s gamma function Γ(x) = ∫ ∞ 0 e−ttx−1 dt (x > 0) is one of the most important functions in analysis and its applications. The history and the development of this function are described in detail in a paper...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2007
ISSN: 0021-9045
DOI: 10.1016/j.jat.2006.04.008