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Multiple Gamma Functions and Their Applications
2014The double Gamma function Γ 2 and the multiple Gamma functions Γ n were defined and studied systematically by Barnes in about 1900. Before their investigation by Barnes, these functions had been introduced in a different form by, for example, Holder, Alexeiewsky, and Kinkelin. Although these functions did not appear in the tables of the most well-known
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Integrals associated with the multiple gamma function
Integral Transforms and Special Functions, 2014The multiple gamma function Γn(z), defined by a recurrence-functional equation as a generalization of the Euler gamma function, is used in many applications of pure and applied mathematics, and theoretical physics. The theory of the multiple gamma function has been related to certain spectral functions in mathematical physics, to the study of ...
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Local adaptive tone mapping with composite multiple gamma functions
2009 16th IEEE International Conference on Image Processing (ICIP), 2009We describe a high-speed method of correcting and compressing the dynamic range of images that can be operated intuitively and naturally. Adaptive operations are conducted for shadow, middle, and highlight tones in the local areas of images. Although natural image processing can be achieved with default parameters, we can set the parameters for each of
Sohsuke Shimoyama +3 more
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Kummer's formula for multiple gamma functions
2006The multiple gamma function is defined as \(\Gamma_r(x)=\exp(\zeta'_r(0, x))\) where \[ \zeta_r(s, x)=\sum_{n_1,\dots,n_r=0}^\infty(n_1+\dots+n_r+x)^{-s} \] is the multiple Hurwitz zeta-function and the differentiation is in the first variable \(s\). Note that \(\Gamma_1(x)=\Gamma(x)/\sqrt{2\pi}\), where \(\Gamma(x)\) is the Euler gamma function. For \(
Kurokawa Nobushige, Koyama Shin-ya
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An elliptic analogue of the multiple gamma function
Journal of Physics A: Mathematical and General, 2001The author introduces an elliptic analogue of Barnes's multiple gamma function, which generalizes the elliptic gamma function of \textit{S. N. M. Ruijsenaars} [J. Math. Phys. 38, No. 2, 1069-1146 (1997; Zbl 0877.39002)]. The fundamental properties of this function are given.
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Antibody–drug conjugates: Smart chemotherapy delivery across tumor histologies
Ca-A Cancer Journal for Clinicians, 2022Paolo Tarantino +2 more
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A review of cancer immunotherapy toxicity
Ca-A Cancer Journal for Clinicians, 2020Lucy Boyce Kennedy
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Genetic testing in prostate cancer management: Considerations informing primary care
Ca-A Cancer Journal for Clinicians, 2022Veda N Giri +2 more
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