Results 11 to 20 of about 1,392,967 (336)
On the Multivariate Gamma-Gamma ($\Gamma \Gamma$) Distribution with Arbitrary Correlation and Applications in Wireless Communications [PDF]
, 2015 The statistical properties of the multivariate Gamma-Gamma ($\Gamma \Gamma$) distribution with arbitrary correlation have remained unknown. In this paper, we provide analytical expressions for the joint probability density function (PDF), cumulative ...
Dai, Linglong +3 more
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Artin formalism for Selberg zeta functions of co-finite Kleinian groups [PDF]
, 2008 Let $\Gamma\backslash\mathbb H^3$ be a finite-volume quotient of the upper-half space, where $\Gamma\subset {\rm SL}(2,\mathbb C)$ is a discrete subgroup.
Brenner, Eliot, Spinu, Florin
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Multiple Gamma Functions and Multiple $q$-Gamma Functions
Publications of the Research Institute for Mathematical Sciences, 1997 We give an asymptotic expansion ( the higher Stirling formula ) and an infinite product representation ( the Weierstrass canonical product representation ) of the Vigneras multiple gamma functions by considering the classical limit of the multiple q
Ueno, Kimio, Nishizawa, Michitomo
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Inequalities for the gamma and q-gamma functions
Journal of Approximation Theory, 2007 \textit{N. Batir} [JIPAM, J. Inequal. Pure Appl. Math. 5, No. 4, Paper No. 97 (2004; Zbl 1078.33001)] found some symmetrical upper and lower bounds for \(\Gamma(x)\) in terms of \(\psi(x)\). In this study, the authors improved Batir's results by getting sharp inequalities.
Alzer, Horst, Grinshpan, Arcadii Z.
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A Ces\`aro Average of Goldbach numbers [PDF]
, 2012 Let $\Lambda$ be the von Mangoldt function and $(r_G(n) = \sum_{m_1 + m_2 = n} \Lambda(m_1) \Lambda(m_2))$ be the counting function for the Goldbach numbers. Let $N \geq 2$ be an integer.
Languasco, Alessandro +1 more
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The Minimum in the Gamma Function [PDF]
Nature, 1935 IT is well known that the gamma function “(z) for real and positive values of z has a minimum between z = 1.46 and 1.47. In a number of texts on the theory of functions it is stated that the minimum occurs at z = 1.4616321 and that the corresponding value of “(z) is 0.8856032 Only one text that we have examined, namely Joseph Edwards's monumental work ...
Deming, W. Edwards, Colcord, Clarence G.
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Completely monotonic functions involving the gamma and $q$-gamma functions [PDF]
Proceedings of the American Mathematical Society, 2005 The authors provide new examples of logarithmically completely monotonic functions. These examples are ratios of products involving the Gamma function or the \(q\)-Gamma function. As an application of these results new examples of infinitely divisible probability distributions can be obtained.
Grinshpan, Arcadii Z. +1 more
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The density structure and star formation rate of non-isothermal polytropic turbulence [PDF]
, 2015 The interstellar medium of galaxies is governed by supersonic turbulence, which likely controls the star formation rate (SFR) and the initial mass function (IMF).
Banerjee, Supratik, Federrath, Christoph
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Inverses of Gamma Functions [PDF]
Constructive Approximation, 2014 Euler's Gamma function $ $ either increases or decreases on intervals between two consequtive critical points. The inverse of $ $ on intervals of increase is shown to have an extension to a Pick-function and similar results are given on the intervals of decrease, thereby answering a question by Uchiyama. The corresponding integral representations are
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A Note on Gamma Functions [PDF]
Mathematical Notes, 1959 Various improvements in the formulawhich was discovered by Wallis in 1669, were studied by D. K. Kazarinoff in No. 40 of these Notes (December 1956).
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