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Some Monotonicity Properties of the q-Gamma Function [PDF]
, 2005 We prove some properties of completely monotonic functions and apply them to obtain new results on gamma and q-gamma ...
Gao, Peng
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Three Classes of Logarithmically Completely Monotonic Functions Involving Gamma and Psi Functions [PDF]
, 2006 By a simple approach, two classes of functions involving Euler’s gamma function and originating from certain problems of traffic flow are proved to be logarithmically completely monotonic and a class of functions involving the psi function is showed ...
Qi, Feng
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Experimental Measurements and Computer Simulation of Fission Product Gamma-Ray Spectra [PDF]
, 1997 Airborne gamma ray spectrometry using high volume scintillation detectors, optionally in conjunction with Ge detectors, has potential for making rapid environmental measurements in response to nuclear accidents. An experimental investigation and computer
Sanderson, D.C.W. +4 more
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Certain Logarithmically N-Alternating Monotonic Functions Involving Gamma and q-Gamma Functions [PDF]
, 2005 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.
Qi, Feng
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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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The Best Bounds in Kershaw's Inequality and Two Completely Monotonic Functions [PDF]
, 2006 A new proof for monotonicity and convexity of a function deduced from Kershaw’s inequality involving the Wallis’ function about the Euler’s gamma function is provided.
Qi, Feng
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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.
Horst Alzer, Arcadii Z. Grinshpan
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The gamma function via interpolation [PDF]
Numerical Algorithms, 2021 19 ...
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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
Ueno, Kimio, Nishizawa, Michitomo
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On Complex Gamma-Function Integrals [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2020 It was observed recently that relations between matrix elements of certain operators in the ${\rm SL}(2,\mathbb R)$ spin chain models take the form of multidimensional integrals derived by R.A. Gustafson. The spin magnets with ${\rm SL}(2,\mathbb C)$ symmetry group and ${\rm L}_2(\mathbb C)$ as a local Hilbert space give rise to a new type of $Γ ...
Derkachov, Sergey É. +1 more
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