Polylogarithm function li
WebThe logarithmic integral function (the integral logarithm) uses the same notation, li(x), but without an index. The toolbox provides the logint function to compute the logarithmic integral function. Floating-point evaluation of the polylogarithm function can be slow for complex arguments or high-precision numbers. WebWe give an overview of the representation and many connections between integrals of products of polylogarithmic functions and Euler sums. We shall consider polylogarithmic functions with linear, quadratic, and trigonometric arguments, thereby producing new results and further reinforcing the well-known connection between Euler sums and …
Polylogarithm function li
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WebThe functions Lin(z) are de ned on Cpnf1g. If Lis a nitely rami ed extension of Qpthen the limit limz!1 z2L Lin(z) exists for n 2, and is independent of L. Using this limit as the value for Lin at 1, Lin extends to a function on Cp, which is continuous on nitely rami ed extensions of Qp. If mand nare integers at least equal to 2, then on Cp WebApr 10, 2024 · The dilogarithm (or Spence’s function [1]) [2,3] is defined as Li 2(z)= X ... resembles the Dirichlet series for the polylogarithm function Li s(z). Nice reviews of the theory of such functions are given by Lewin [2,19] and Berndt [10].
WebOct 7, 2010 · We present a compact analytic formula for the two-loop six-particle maximally helicity violating remainder function (equivalently, the two-loop lightlike hexagon Wilson loop) in N = 4 supersymmetric Yang-Mills theory in terms of the classical polylogarithm functions Li k with cross ratios of momentum twistor invariants as their arguments. In … WebJan 22, 2024 · Description. Compute the polylogarithm function Li_s (z) , initially defined as the power series, Li_ {s+1} (z) = Int [0..z] (Li_s (t) / t) dt. Currently, mainly the case of …
WebThe polylogarithm function, Li p (z), is defined, and a number of algorithms are derived for its computation, valid in different ranges of its real parameter p and complex argument z. … WebThe logarithmic integral function (the integral logarithm) uses the same notation, li(x), but without an index. The toolbox provides the logint function to compute the logarithmic integral function. Floating-point evaluation of …
Webgives the Nielsen generalized polylogarithm function . Details. Mathematical function, suitable for both symbolic and numerical manipulation.. . . PolyLog [n, z] has a branch cut …
WebAn alternative way of generating Li−n(z) for any n would be to make use of the generating function method, i.e. to generate {Li−n(z)}∞ n=1 from a single function of two variables G(z,t) by repeated differentiation of that function. It is fortunate that there are several such functions (of which (2.6a) and (2.6b) could be found in 高校受験 ある国WebFeb 3, 2024 · Integrals of inverse trigonometric and polylogarithmic functions. In this paper we study the representation of integrals whose integrand involves the product of a … 高校受験 アジアWebMar 24, 2024 · The trilogarithm Li_3(z), sometimes also denoted L_3, is special case of the polylogarithm Li_n(z) for n=3. Note that the notation Li_3(x) for the trilogarithm is unfortunately similar to that for the logarithmic integral Li(x). The trilogarithm is implemented in the Wolfram Language as PolyLog[3, z]. Plots of Li_3(z) in the complex … tartuWebMay 18, 2009 · The nth order polylogarithm Li n (z) is defined for z ≦ 1 by ([4, p. 169], cf. [2, §1. 11 (14) and § 1. 11. 1]). The definition can be extended to all values of z in the z … 高校受験 アプリ 無料 人気WebFor s = 2 s = 2, \mathrm {Li_2 (z)} Li2(z) is also called ‘dilogarithm’ or “Spence's function”. The "default" method uses the dilog or complex_dilog function from package gsl , … 高校受験 あと 30点WebThe polylogarithm Li_n(z), also known as the Jonquière's function, is the function Li_n(z)=sum_(k=1)^infty(z^k)/(k^n) (1) defined in the complex plane over the open unit … 高校受験 あると便利WebThe polylogarithm function, Li p(z), is defined, and a number of algorithms are derived for its computation, valid in different ranges of its real parameter p and complex argument z. … 高校受験 アメブロ