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Polylogarithm

In mathematics, the polylogarithm (also known as Jonquière's function, for Alfred Jonquière) is a special function Lis(z) of order s and argument z. Only for special values of s does the polylogarithm reduce to an elementary function such as the natural logarithm or a rational function. In quantum statistics, the polylogarithm function appears as the…

Relationship to other functions, Overview & Dilogarithm

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Overview

Properties

Particular values

Relationship to other functions

Integral representations

Series representations

Asymptotic expansions

Limiting behavior

Dilogarithm

Polylogarithm ladders

Monodromy

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Map overview Semantic statistics

Polylogarithm

Nodes105
Edges104
Triples186
Avg. degree1.98
Density0.019048
Components1

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Polylogarithm

Top relations

related to Relationship to other functions · 46
Polylogarithm → Abramowitz, Bernoulli, Bn, Boersma, Bose, Ch, Cis, Clausen, Debye, Dempsey, Dirac, Dirichlet, Einstein, Equivalently, Erdélyi, Fermi, For, Gamma, Hurwitz, Im
related to Series representations · 38
Polylogarithm → As, B1, Bernoulli, Bose, By, Einstein, Erdélyi, Erdélyi's, Euler's, For, Gamma, Gradshteyn, Guillera, Hankel, Hn, Hurwitz, If, Im, In, Introducing
related to Integral representations · 36
Polylogarithm → Abel, All, Any, Arndt, As, Boltzmann, Borwein, Bose, Dingle, Dirac, Einstein, Fermi, For, Gamma, Girgensohn, GSL, Hankel, Hermite-type, Hurwitz, Im
related to Particular values · 25
Polylogarithm → Accordingly, All, As, Borwein, Broadhurst, Equivalent, Eulerian, For, For Re, Fourier, Girgensohn, Hurwitz, In, Lewin, Li, Li1, Lis, No, Particular, Riemann
related to External links · 8
Polylogarithm → Algorithms, Analytic Number Theory, Dilogarithm, Eric, GMP-based, GPL-licensed, MathWorld, Weisstein
related to Properties · 8
Polylogarithm → Also, Depending, Im, In, It, Li, Ln, The
related to Dilogarithm · 6
Polylogarithm → Abramowitz, An, Li, Li2, Stegun, The
related to Limiting behavior · 6
Polylogarithm → Gamma, Im, Li, Re, The, Wood
related to Polylogarithm ladders · 5
Polylogarithm → Define, Leonard Lewin, Li, Then, These
related to Asymptotic expansions · 3
Polylogarithm → For, Gamma, Li

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Important terminology

li displaystyle operatorname function ln pi sum integral series gamma infty zeta left integer right mu s-1 -1 frac re

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Polylogarithmis arational function0.90text
Polylogarithmis aspecial case of the incomplete polylogarithm function Li s0.90text
the natural logarithm or a rational functioninstance ofOnly for special values of s does the polylogarithm reduce to an elementary function0.80text
Polylogarithmrelated to Asymptotic expansionsFor0.60section
Polylogarithmrelated to Asymptotic expansionsLi0.60section
Polylogarithmrelated to Asymptotic expansionsGamma0.60section
Polylogarithmrelated to DilogarithmThe0.60section
Polylogarithmrelated to DilogarithmAn0.60section
Polylogarithmrelated to DilogarithmAbramowitz0.60section
Polylogarithmrelated to DilogarithmStegun0.60section
Polylogarithmrelated to DilogarithmLi0.60section
Polylogarithmrelated to DilogarithmLi20.60section

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