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On gamma function inequalities
Scandinavian Actuarial Journal, 1973Watson's method [1] is used to find two convergent monotonically non-decreasing sequences whose upper bounds are equal to Γ(l)Γ(l∓2a)/Γ2(l∓a) ( = K say), provided l > max (0, - 2a). Boyd [2] showed that Gurland's inequality [3] for K corresponds to the first term of the first sequence; Raja Rao's inequality [4] corresponds to the second term of the ...
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An Inequality for Gamma Functions
Canadian Mathematical Bulletin, 1978By using Bellman-Wishart distribution, Bellman [1], an inequality for gamma functions is derived. This inequality generalizes a recent inequality given by Selliah [4].
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Multiple Gamma and related functions
Applied Mathematics and Computation, 2003The authors give several new (and potentially useful) relationships between the multiple Gamma functions and other mathematical functions and constants. As by-products of some of these relationships, a classical definite integral due to Euler and other definite integrals are also considered together with closed-form evaluations of some series involving
Junesang Choi +2 more
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On the Formalization of Gamma Function in HOL
Journal of Automated Reasoning, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Umair Siddique, Osman Hasan
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The Gamma Function and the Incomplete Gamma Functions
2017The gamma function is defined for \(s \in \mathbb{C}\) by $$\displaystyle{ \varGamma \left (s\right ) =\int _{ 0}^{\infty }t^{s-1}e^{-t}dt }$$
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Canadian Journal of Mathematics, 1954
The gamma function Γ(z + 1) = П(z) has been defined in different ways:(1)(Weierstrass)(2)(Kuler)(3)(Gauss)(4)(Euler)(5)(Lerch)
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The gamma function Γ(z + 1) = П(z) has been defined in different ways:(1)(Weierstrass)(2)(Kuler)(3)(Gauss)(4)(Euler)(5)(Lerch)
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Numerical Algorithms, 2008
Some new inequalities for Euler's gamma function are derived and proved.
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Some new inequalities for Euler's gamma function are derived and proved.
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Rendiconti del Circolo Matematico di Palermo, 1999
Inequalities and convexity properties known for the gamma function are extended to the qgamma function, 0<q<1 . Applying some classical inequalities for convex functions, we deduce monotonicity results for several functions involving the qgamma function. Further applications to the probability theory are given.
Elezović, N. +2 more
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Inequalities and convexity properties known for the gamma function are extended to the qgamma function, 0<q<1 . Applying some classical inequalities for convex functions, we deduce monotonicity results for several functions involving the qgamma function. Further applications to the probability theory are given.
Elezović, N. +2 more
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Continued Fraction Approximation for the Gamma Function by the Tri-gamma Function
Results in Mathematics, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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