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The dilogarithm function

WebJan 4, 2024 · Let ${\\rm Li}_2$ denote the dilogarithm function. Evaluate the integral $$\\mathcal{J} = \\int_{0}^{1} \\frac{\\log^2(1-x) {\\rm Li}_2(-x)}{x} \\, {\\rm d}x $$ A ... WebThe dilogarithm function, also referred to as the Spence function, has a long history connected with some of the great names in the history of mathematics. The integral that de¯ nes it ¯ rst appears in one of the letters from Leibniz to Johann Bernoulli

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WebJan 1, 2007 · The Dilogarithm Function Authors: Don Zagier Abstract The dilogarithm function, defined in the first sentence of Chapter I, is a function which has been known for more than 250 years, but... WebThe dilogarithm function for complex argument Maximon, Leonard C. This paper summarizes the basic properties of the Euler dilogarithm function, often referred to as the Spence function. party bus rental huntsville al https://jdgolf.net

On the Accessibility of Khoi’s Dilogarithm Identity Involving the ...

WebOct 8, 2016 · We use the standard notation $\operatorname{Li}_2$ for the dilogarithm function and $\zeta$ for the Riemann zeta function.For $ z <1$, we have $$ \operatorname{Li}_2\left(2z-z^2\right) = -\ln^2\left(2-z\right)+\zeta(2)-2\operatorname{Li}_2\left(\frac{1}{2-z}\right)+2\operatorname{Li}_2(z). $$ This result … WebIn the case of the dilogarithm, the group of anharmonic ratios allows one to reduce the computation in the general case to a fundamental region for that group. WebThe dilogarithm is a special case of the polylogarithmfor . Note that the notation is unfortunately similar to that for the logarithmic integral. There are also two different commonly encountered normalizations for the function, both denoted , and one of which … The Riemann zeta function is an extremely important special function of … Wolfram, creators of the Wolfram Language, Wolfram Alpha, Mathematica, … For any base, the logarithm function has a singularity at .In the above plot, the blue … where is the Dirichlet beta function, is Legendre's chi-function, is the Glaisher … An unsolved problem in mathematics attributed to Lehmer (1933) that … References Cvijović, D. and Klinowski, J. "Closed-Form Summation of Some … Abel's Duplication Formula, Dilogarithm, Functional Equation, Polylogarithm, … See also Dilogarithm, Spence's Function Explore with Wolfram Alpha. More things … tina stanley portland maine

special functions - Short calculation of the dilogarithm?

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The dilogarithm function

Spence

Web我正在從C切換到C ++，並且我想最佳地使用可用的附加功能，並避免使用諸如void *指針之類的“ C風格”東西。 具體來說，我正在嘗試制作類似gsl_function的接口（不是在C ++中使用gsl的包裝器）。. 在C語言中，我編寫了一些用於根查找，集成的例程，這些例程使用類似gsl_function的接口將數學函數傳遞給 ... WebAdditive blending of local approximations into a globally-valid approximation with application to the dilogarithm

The dilogarithm function

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WebJan 1, 2007 · It should be noted that the dilogarithm function is available as a built-in function in most well-known mathematical software tools such as MATLAB and MATHEMATICA. Besides, there exist... WebWe show new integral representations for dilogarithm and trilogarithm functions on the unit interval. As a consequence, we also prove (1) new integral representations for Apéry, Catalan constants and Legendre \(\chi\) functions of order 2, 3, (2) a lower bound for the dilogarithm function on the unit interval, (3) new Euler sums.

WebThe dilogarithm function for complex argument By Leonard C. Maximon Department of Physics, The George Washington University, Washington, DC 20052, USA ([email protected]) … In mathematics, Spence's function, or dilogarithm, denoted as Li2(z), is a particular case of the polylogarithm. Two related special functions are referred to as Spence's function, the dilogarithm itself: and its reflection. For z &lt; 1, an infinite series also applies (the integral definition constitutes its analytical extension to the complex plane):

WebAug 20, 1994 · Anatol N. Kirillov We study the dilogarithm identities from algebraic, analytic, asymptotic, -theoretic, combinatorial and representation-theoretic points of view. We prove that a lot of dilogarithm identities (hypothetically all !) can be … WebSoluciona tus problemas matemáticos con nuestro solucionador matemático gratuito, que incluye soluciones paso a paso. Nuestro solucionador matemático admite matemáticas básicas, pre-álgebra, álgebra, trigonometría, cálculo y mucho más.

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party bus rental fargo ndWebThe dilogarithm function for complex argument BY LEONARD C. MAXIMON Department of Physics, The George Washington University, Washington, DC 20052, USA ([email protected]) … tina stanley associatesWebThe dilogarithm function is defined as Li 2(z) := P∞ k=1 zk 2, which converges for all complex zwith z ≤ 1. In this note, we derive new and nontrivial two-term dilogarithm identities, improving upon remarkable discoveries due to Lima [11]. The natural logarithm function, as defined for positive values, is, of course, very fun- party bus rental greensboro ncWebthe Liouville action, and the dilogarithm Joint AMS-MAA National Meeting Ettore Aldrovandi Dept. of Mathematics Florida State University Baltimore, January 16, 2003. Riemann Surfaces and constant (= −1) negative curvature metrics X compact Riemann surface, genus ≥ 2. Conformal metric: party bus rental hattiesburgWebAbstract. The dilogarithm function, defined in the first sentence of Chapter I, is a function which has been known for more than 250 years, but which for a long time was familiar … party bus rental fayetteville arWebJun 19, 2024 · The Dilogarithm Function in Geometry and Number Theory (Pt. 3) Laboratory of Axiomatics Seminar. Abstract: In this third part, we explore more the connections of the Bloch-Wigner dilogarithm with volumes of hyperbolic 3-manifolds. Specifically, we will express the volume of a hyperbolic 3-manifold as a finite sum of Bloch-Wigner dilogarithms. party bus rental henderson nevadaWebNov 8, 2003 · This paper summarizes the basic properties of the Euler dilogarithm function, often referred to as the Spence function. These include integral representations, series … party bus rental grand forks nd