Everything about Polylogarithm
Special mathematical function
In mathematics, the polylogarithm (also known as JonquiĆØre's function, for Alfred JonquiĆØre) 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 closed form of integrals of the FermiāDirac distribution and the BoseāEinstein distribution, and is also known as the FermiāDirac integral or the BoseāEinstein integral. In quantum electrodynamics, polylogarithms of positive integer order arise in the calculation of processes represented by higher-order Feynman diagrams. Wikipedia ā
š§ Start here: a 6-step reading path
- Read the overview: PolylogarithmA 5-minute orientation
- Skim a recent paper: Convex Families of q-Derivative Meromorphic Functions Involving the Polylogarithm FunctionInfluential work since 2022
- Pick up a classic book: String-Math 2012The most-reprinted book on the subject
- Read the landmark paper: The Bloch-Wigner-Ramakrishnan polylogarithm functionCited 86 times
- Go sideways: Lerch transcendentA closely related topic
- Go sideways: DilogarithmA closely related topic
š Definitions
Noun A function of complex numbers related to logarithms.
š Landmark papers (most cited)
The Bloch-Wigner-Ramakrishnan polylogarithm function
Polylogarithm identities in a conformal field theory in three dimensions
Euler sums and integrals of polylogarithm functions
Evaluating multiple polylogarithm values at sixth roots of unity up to weight six
The Bergman kernel of the FockāBargmannāHartogs domain and the polylogarithm function
Classical Motivic Polylogarithm According to Beilinson and Deligne
Standard relations of multiple polylogarithm values at roots of unity
New integral representations of the polylogarithm function
š Influential since 2022
Convex Families of q-Derivative Meromorphic Functions Involving the Polylogarithm Function
Contour integrations and parity results of cyclotomic Euler sums and multiple polylogarithm function
The Cotangent Function as an Avatar of the Polylogarithm Function of Order 0 and Ramanujanās Formula
SOME PROPERTIES OF ANALYTIC FUNCTIONS DEFINED BY POLYLOGARITHM FUNCTIONS
Carlitz operators and higher polylogarithm identities
š Books worth reading
- šString-Math 2012Germany) String-Math (Conference) (2012 Bonn Ā· 2015
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
š Related topics
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