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Studies on multiple zeta values, Arakawa-Kaneko zeta functions and iterated log-sine integrals

Studies on multiple zeta values, Arakawa-Kaneko zeta functions and iterated log-sine integrals
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Multiple sine functions

Forum Mathematicum, 2003
This paper is an English version of a part of some lecture notes by N. Kurokawa from 1991, the notes having been taken by S. Koyama. In the paper, a theory of multiple sine functions is constructed which generalizes the usual sine function. The double sine function was introduced by Hölder in 1886, and the authors introduce the triple and higher sine ...
Kurokawa Nobushige, Koyama Shin-ya
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Differential Algebraicity of Multiple Sine Functions

Letters in Mathematical Physics, 2005
Let \(w_1,\dots, w_r> 0\). The multiple sine function of period \(\underline w= (w_1,\dots, w_r)\) is defined by \[ S_r(x,\underline w)= \Gamma_r(x,\underline w)^{-1} \Gamma_r(|\underline w|- x,\underline w)^{-1)^r}, \] where \(|\underline w|= w_1+\cdots+ w_r\), and \(\Gamma_r(x,\underline w)\) is the multiple gamma function originally studied by ...
Kurokawa, Nobushige, Wakayama, Masato
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Multiple gamma functions, multiple sine functions, and Appell’s O-functions

The Ramanujan Journal, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A modified sine cosine algorithm for accurate global optimization of numerical functions and multiple hydropower reservoirs operation

Knowledge-Based Systems, 2020
Abstract Sine cosine algorithm (SCA) is an emerging meta-heuristic method for the complicated global optimization problems, but still suffers from the premature convergence problem due to the loss of swarm diversity. To improve the SCA performance, this paper develops a modified sine cosine algorithm coupled with three improvement strategies, where ...
Zhong-kai Feng, Shuai Liu, Wen-jing Niu, Bao-jian Li, Wen-chuan Wang, Bin Luo, Shu-min Miao   +6 more
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Some applications of the Gamma and polygamma functions involving convolutions of the Rayleigh functions, multiple Euler sums and log‐sine integrals

Mathematische Nachrichten, 2009
AbstractThe Gamma function and its n th logarithmic derivatives (that is, the polygamma or the psi‐functions) have found many interesting and useful applications in a variety of subjects in pure and applied mathematics. Here we mainly apply these functions to treat convolutions of the Rayleigh functions by recalling a general identity expressing a ...
Choi, Junesang, Srivastava, H. M.
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GENERALIZED MAHLER MEASURES AND MULTIPLE SINE FUNCTIONS

International Journal of Mathematics, 2004
We introduce a generalized Mahler measure. It has relations to multiple sine functions and Dirichlet L-functions. In particular, we are able to express special values of Dirichlet L-functions by sum of logarithmic generalized Mahler measures.
Gon, Yasuro, Oyanagi, Hideo
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Shintani’s prehomogeneous zeta functions and multiple sine functions

Rendiconti del Circolo Matematico di Palermo, 2005
For \(n\geq 1\) let \(Z_n(s)\) be Shintani's prehomogeneous zeta function associated to the space of symmetric matrices. The author proves that for \(n\equiv 1\pmod 4\), \(n\neq 1\), the function \( Z_n(s)\) has a simple zero at \(s=0\), and \[ Z_n'(0)=-(-4)^{\frac{1-n}{4}}(\zeta(-1)\zeta(-3)\dots \zeta(-(n-2)))^2\log\left(\prod_{k=1}^{\frac{n-1}{4}}S_{
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BEHAVIOR OF SOME GENERALIZED MULTIPLE SINE FUNCTIONS

International Journal of Number Theory, 2008
Our aim is to investigate the behavior of generalized multiple sine functions with general period parameters in the fundamental domain. For that, we need to calculate the number of their extremal values. By estimating their special values, we determine it in some cases including the quintuple sine function. As a consequence, we sketch their graphs.
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Warming substantiated by multiple sine functions decomposition of multiple cities' temperature data

2015 Chinese Automation Congress (CAC), 2015
In recent years, extensive efforts have been committed to the temperature forecast work, and more and more studies have indicated that the temperature is rising. For the purpose of forecasting long-term temperature trend, a temperature forecast method named multiple sine functions decomposition (MSFD) method is presented in this paper.
Yunong Zhang, null Jingyao Ma, null Binbin Qiu, null Sitong Ding, null Zhi Yang   +4 more
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