Polylogarithm function li
Web14. We know some exact values of the trilogarithm function. Known real analytic values for : where is the Apéry's constant. where is the golden ratio. Using identities for the list above we could also get: or we could write into this alternate form. or there is an alternate form here. We know even less about complex argumented values: WebThe code is aimed at calculating Li_s(z) for all (complex) s and z. This is still a little experimental, but there is a fairly large test set that all works nicely. Note that the aimed …
Polylogarithm function li
Did you know?
WebApr 12, 2024 · In this paper, we introduce and study a new subclass S n β,λ,δ,b (α), involving polylogarithm functions which are associated with differential operator. we also obtain … WebPolylogarithm Function Description. Computes the n-based polylogarithm of z: Li_n(z). Usage polylog(z, n) Arguments. z: real number or vector, all entries satisfying abs(z)<1. n: …
WebFeb 14, 2024 · This formula is straightforward to prove. Given the usual inversion formula for L i 2. ( ⋆) L i 2 ( − z) + L i 2 ( − z − 1) = − π 2 6 − 1 2 log 2 ( z) Divide by z, integrate both … WebMar 24, 2024 · The function reduces to the usual polylogarithm for the case S_(n-1,1)(z)=Li_n(z). The Nielsen generalized polylogarithm is implemented as PolyLog[n, p, z]. TOPICS
WebThe 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 ... Webdict.cc German-English Dictionary: Translation for legale Funktion
WebApr 23, 2024 · The probability generating function of \( N \) can be expressed in terms of the polylogarithm function \( \Li \) that was introduced in the section on the exponential-logarithmic distribution. Recall that the polylogarithm of order \( s \in \R \) is defined by \[ \Li_s(x) = \sum_{k=1}^\infty \frac{x^k}{k^s}, \quad x \in (-1, 1) \]
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 … is there a dominican republic dating siteWebOct 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 … i hop out at yo party im with the gangWebThe 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. … ihop order online to goWebIf Li s denotes the polylogarithm of order s, where s is a natural num- ... MSC: 11M35, 33E20, 40A25, 40B05. Keywords: Multiple harmonic series, Lerch function, Polylogarithm. Introduction Equalities and identities between multiple harmonic series and polyloga-rithms have been investigated by many authors; see for instance [1] and the is there a dove season in michiganWebWe can avoid the need for complex arithmetic in this case by substituting the expression: ∫ 0 x t 3 d t e t − 1 = − 6 Li 4 ( e − x) − 6 x Li 3 ( e − x) − 3 x 2 Li 2 ( e − x) − x 3 Li 1 ( e − x) + π 4 … i hop-o\\u0027-my-thumbWebMar 19, 2024 · Abstract: In this paper, we give explicit evaluation for some integrals involving polylogarithm functions of types $\int_{0}^{x}t^{m} Li_{p}(t)\mathrm{d}t$ and … is there a dot after missWebThis function is defined in analogy with the Riemann zeta function as providing the sum of the alternating series. η ( s) = ∑ k = 0 ∞ ( − 1) k k s = 1 − 1 2 s + 1 3 s − 1 4 s + …. The eta … is there a doomsday clock