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Several nice inequalities between gamma function and the truncations of its asymptotic series can be found in [28, 29].
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Γ and ϒ denote gamma function and incomplete gamma function.
where is the Gamma function and.
where is the Gamma function,, and is the lower incomplete Gamma function,.
Here (Gamma(t)) is the Gamma function and its definition is (Gamma(t)=int_{0}^{infty}e^{-x}x^{t-1},dx).
Let (Gamma(cdot)) be the gamma function and let (alpha>0) be a real number.
where Γ(M) and G M, x) denote the Gamma function and the regularized Gamma function [33], respectively.
Taking the logarithmic derivative of the double gamma function and triple gamma function, respectively, the following result is immediate.
The Q-function, gamma function, and incomplete gamma function are denoted by Q x), Γ(a), and Γ a, x), respectively.
First, we give the following inequalities, which include the gamma function and a trigonometric function.
where Γ is the Euler Gamma function and. is the discrete power function.
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