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- Polylogarithm abstract "In mathematics, the polylogarithm (also known as Jonquière's function) 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 rational functions. In quantum statistics, the polylogarithm function appears as the closed form of integrals of the Fermi–Dirac distribution and the Bose–Einstein distribution, and is also known as the Fermi–Dirac integral or the Bose–Einstein integral. In quantum electrodynamics, polylogarithms of positive integer order arise in the calculation of processes represented by higher-order Feynman diagrams.The polylogarithm function is equivalent to the Hurwitz zeta function — either function can be expressed in terms of the other — and both functions are special cases of the Lerch transcendent. Polylogarithms should not be confused with polylogarithmic functions nor with the offset logarithmic integral which has a similar notation. The polylogarithm function is defined by the infinite sum, or power series:This definition is valid for arbitrary complex order s and for all complex arguments z with |z| < 1; it can be extended to |z| ≥ 1 by the process of analytic continuation. The special case s = 1 involves the ordinary natural logarithm, Li1(z) = −ln(1−z), while the special cases s = 2 and s = 3 are called the dilogarithm (also referred to as Spence's function) and trilogarithm respectively. The name of the function comes from the fact that it may also be defined as the repeated integral of itself:thus the dilogarithm is an integral of the logarithm, and so on. For nonpositive integer orders s, the polylogarithm is a rational function.".
- Polylogarithm thumbnail Complex_polylogminus3.jpg?width=300.
- Polylogarithm wikiPageExternalLink Vol1.pdf.
- Polylogarithm wikiPageExternalLink item?id=BSMF_1889__17__142_1.
- Polylogarithm wikiPageExternalLink digits.pdf.
- Polylogarithm wikiPageExternalLink 93_001-Borwein-Borwein-Girgensohn.pdf.
- Polylogarithm wikiPageExternalLink zagier.pdf.
- Polylogarithm wikiPageExternalLink 2807.full.pdf.
- Polylogarithm wikiPageExternalLink 897.full.pdf.
- Polylogarithm wikiPageExternalLink oeuvres_completes_de_abel_nouv_ed_2_kap14_opt.pdf.
- Polylogarithm wikiPageExternalLink S0002-9939-97-04102-6.pdf.
- Polylogarithm wikiPageExternalLink 110.
- Polylogarithm wikiPageExternalLink 1.html.
- Polylogarithm wikiPageExternalLink SEC117.
- Polylogarithm wikiPageExternalLink anant.
- Polylogarithm wikiPageID "482471".
- Polylogarithm wikiPageRevisionID "594681948".
- Polylogarithm authorlink "Don Zagier".
- Polylogarithm first "Don".
- Polylogarithm first "T.M.".
- Polylogarithm hasPhotoCollection Polylogarithm.
- Polylogarithm id "25.12".
- Polylogarithm last "Apostol".
- Polylogarithm last "Zagier".
- Polylogarithm ref "harv".
- Polylogarithm title "Dilogarithm".
- Polylogarithm title "Polylogarithm".
- Polylogarithm urlname "Dilogarithm".
- Polylogarithm urlname "Polylogarithm".
- Polylogarithm year "1989".
- Polylogarithm subject Category:Rational_functions.
- Polylogarithm subject Category:Special_functions.
- Polylogarithm subject Category:Zeta_and_L-functions.
- Polylogarithm type Abstraction100002137.
- Polylogarithm type Function113783816.
- Polylogarithm type MathematicalRelation113783581.
- Polylogarithm type RationalFunctions.
- Polylogarithm type Relation100031921.
- Polylogarithm type SpecialFunctions.
- Polylogarithm comment "In mathematics, the polylogarithm (also known as Jonquière's function) 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 rational functions. In quantum statistics, the polylogarithm function appears as the closed form of integrals of the Fermi–Dirac distribution and the Bose–Einstein distribution, and is also known as the Fermi–Dirac integral or the Bose–Einstein integral.".
- Polylogarithm label "Fonction polylogarithme".
- Polylogarithm label "Función polilogarítmica".
- Polylogarithm label "Função polilogarítmica".
- Polylogarithm label "Polilogaritmo".
- Polylogarithm label "Polilogarytm".
- Polylogarithm label "Polylogarithm".
- Polylogarithm label "Polylogarithmus".
- Polylogarithm label "Полилогарифм".
- Polylogarithm label "多重对数函数".
- Polylogarithm label "多重対数関数".
- Polylogarithm sameAs Polylogarithmus.
- Polylogarithm sameAs Función_polilogarítmica.
- Polylogarithm sameAs Fonction_polylogarithme.
- Polylogarithm sameAs Polilogaritmo.
- Polylogarithm sameAs 多重対数関数.
- Polylogarithm sameAs 다중로그.
- Polylogarithm sameAs Polilogarytm.
- Polylogarithm sameAs Função_polilogarítmica.
- Polylogarithm sameAs m.02fv4v.
- Polylogarithm sameAs Q1238449.
- Polylogarithm sameAs Q1238449.
- Polylogarithm sameAs Polylogarithm.
- Polylogarithm wasDerivedFrom Polylogarithm?oldid=594681948.
- Polylogarithm depiction Complex_polylogminus3.jpg.
- Polylogarithm isPrimaryTopicOf Polylogarithm.
