Results 41 to 50 of about 562 (207)
High Risk, Low Reward: A Challenge to the Astronomical Value of Existential Risk Mitigation
, 2023 Philosophy &Public Affairs, Volume 51, Issue 4, Page 373-412, Fall 2023.
David Thorstad
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Nielsen’s Generalized Polylogarithms [PDF]
SIAM Journal on Mathematical Analysis, 1986 Properties (in particular functional relations and special values) of the functions \[ (-1)^{n+p-1}(n-1)! p! S_{n,p}(z)=\int^{1}_{0}\log^{n-1}t \log^ p(1-zt)(dt/t), \] \[ (-1)^{n+p-1}(n-1)! p! L_{n,p}(z)=\int^{z}_{0}\log^{n-1}t \log^ p(1-t)(dt/t), \] \[ (-1)^{n-1}(n-1)! p!
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Fractal and Fractional, 2023 In this paper, we consider an approximation of the Caputo fractional derivative and its asymptotic expansion formula, whose generating function is the polylogarithm function.
Yuri Dimitrov +2 more
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ON A CERTAIN CONVOLUTION OF POLYLOGARITHMS [PDF]
Bulletin of the Australian Mathematical Society, 2011 AbstractIn this paper, we consider certain double series analogous to Tornheim’s double series and real analytic Eisenstein series. By computing double integrals in two ways, we express the double series as a sum of products of polylogarithms. The technique generalises one given by Kanemitsu, Tanigawa and Yoshimoto.
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Polylogarithms and the Asymptotic Formula for the Moments of Lebesgue’s Singular Function
Моделирование и анализ информационных систем, 2016 Recall the Lebesgue's singular function. We define a Lebesgue's singular function \(L(t)\) as the unique continuous solution of the functional equation$$L(t) = qL(2t) +pL(2t-1),$$where \(p,q>0\), \(q=1-p\), \(p\ne q\).The moments of Lebesque' singular
E. A. Timofeev
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Relations for Nielsen polylogarithms
Journal of Approximation Theory, 2015 The multiple polylogarithms are defined by \[ \text{Li}_{a_1,\dots,a_k}(x)= \sum_{n_1>\cdots> n_k} {x^{n_1}\over n^{a_1}_1\cdots n^{a_k}_k}. \] The sum \(w= a_1+\cdots+ a_n\) is called the weight of the function. The authors consider also two associated multiple special functions: the multiple Claussen functions \[ \text{Cl}_{a_1,\dots,a_k}(\tau ...
Jonathan M. Borwein, Armin Straub
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Degenerate polyexponential functions and type 2 degenerate poly-Bernoulli numbers and polynomials
Advances in Difference Equations, 2020 The polyexponential functions were introduced by Hardy and rediscovered by Kim, as inverses to the polylogarithm functions. Recently, the type 2 poly-Bernoulli numbers and polynomials were defined by means of the polyexponential functions. In this paper,
Taekyun Kim +3 more
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Journal of High Energy Physics, 2023 We studied the two-loop non-factorizable Feynman diagrams for the t-channel single-top production process in quantum chromodynamics. We present a systematic computation of master integrals of the two-loop Feynman diagrams with one internal massive ...
Zihao Wu, Ming-Ming Long
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The Polylogarithm Function in Julia
CoRR, 2020 The polylogarithm function is one of the constellation of important mathematical functions. It has a long history, and many connections to other special functions and series, and many applications, for instance in statistical physics. However, the practical aspects of its numerical evaluation have not received the type of comprehensive treatments ...
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Hurwitz-Lerch Type Multi-Poly-Cauchy Numbers
Mathematics, 2019 In this paper, we define Hurwitz–Lerch multi-poly-Cauchy numbers using the multiple polylogarithm factorial function. Furthermore, we establish properties of these types of numbers and obtain two different forms of the explicit formula using ...
Noel Lacpao +2 more
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