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...

In mathematics, the incomplete polylogarithm function is related to the polylogarithm function. It is sometimes known as the incomplete Fermi–Dirac integral...

hypergeometric function of Kummer. Another one, defined below, is related to the polylogarithm. Both are named for Ernst Kummer. Kummer's function is defined by Λ...

Spence's function), denoted as Li2(z), is a particular case of the polylogarithm. Two related special functions are referred to as Spence's function...

imq}}{m^{s}}}=\operatorname {Li} _{s}\left(e^{2\pi iq}\right)} where Lis(z) is the polylogarithm. It obeys the duplication formula 2 1 − s F ( s ; q ) = F ( s , q 2...

where Li s ⁡ ( z ) {\displaystyle \operatorname {Li} _{s}(z)} is the polylogarithm. Its derivative is d F j ( x ) d x = F j − 1 ( x ) , {\displaystyle...

resembles the Dirichlet series for the polylogarithm, and, indeed, is trivially expressible in terms of the polylogarithm as χ ν ( z ) = 1 2 [ Li ν ⁡ ( z )...

function. Li s ⁡ ( z ) {\displaystyle \operatorname {Li} _{s}(z)} is a polylogarithm. ( n k ) {\displaystyle n \choose k} is binomial coefficient exp ⁡ (...

{\displaystyle j} . This is an alternate definition of the incomplete polylogarithm, since: F j ⁡ ( x , b ) = 1 Γ ( j + 1 ) ∫ b ∞ t j e t − x + 1 d t =...

series, and various other forms. It is intimately connected with the polylogarithm, inverse tangent integral, polygamma function, Riemann zeta function...

special function that generalizes the Hurwitz zeta function and the polylogarithm. It is named after Czech mathematician Mathias Lerch, who published...

where Li s ⁡ ( z ) {\displaystyle \operatorname {Li} _{s}(z)} is the Polylogarithm. ∫ 0 ∞ sin ⁡ m x e 2 π x − 1 d x = 1 4 coth ⁡ m 2 − 1 2 m {\displaystyle...

Polylogarithm and related functions: Incomplete polylogarithm Clausen function Complete Fermi–Dirac integral, an alternate form of the polylogarithm....

formulas for special values of Dedekind zeta functions in terms of polylogarithm functions. He discovered a short and elementary proof of Fermat's theorem...

the country code top level domain (ccTLD) for Liechtenstein Li, the polylogarithm function Li, the logarithmic integral function <li></li>, indicating...

Pollard's kangaroo algorithm Pollard's rho algorithm for logarithms Polylogarithm Polylogarithmic function Prime number theorem Richter magnitude scale...

arXiv:0912.3844 [math.CA]. Crandall, Richard. "Unified algorithms for polylogarithm, L-series, and zeta variants" (PDF). PSI Press. Archived from the original...

whose field of study is hyperbolic geometry, geometric group theory and polylogarithm identities. As a child, she went to a gymnasium in Basel and then studied...

related functions see the articles zeta function and L-function. The polylogarithm is given by Li s ⁡ ( z ) = ∑ k = 1 ∞ z k k s {\displaystyle \operatorname...

algebraic geometry as differential forms with logarithmic poles. The polylogarithm is the function defined by Li s ⁡ ( z ) = ∑ k = 1 ∞ z k k s . {\displaystyle...

i s ( z ) {\displaystyle \mathrm {Li} _{s}(z)} is the polylogarithm function. The polylogarithm term must always be positive and real, which means its...

{\frac {1}{\operatorname {Li} _{s}(x)}}} for s > 1 where Lis(x) is the polylogarithm. For x = 1 the product above is just ⁠1/ζ(s)⁠. Many well known constants...

1957), Swiss expert on hyperbolic geometry, geometric group theory and polylogarithm identities Christine Kelley, American coding theorist, director of Project...

function Nicholas Mercator – first to use the term natural logarithm Polylogarithm Von Mangoldt function Including C, C++, SAS, MATLAB, Mathematica, Fortran...

the special case of the integral formula for the Nielsen generalized polylogarithm function defined in) ∑ n ≥ 0 f n ( n + 1 ) s z n = ( − 1 ) s − 1 ( s...

Bk appearing in the series for tanh x are the Bernoulli numbers. The polylogarithms have these defining identities: Li 2 ( x ) = ∑ n = 1 ∞ 1 n 2 x n Li...

These values can also be regarded as special values of the multiple polylogarithms. The k in the above definition is named the "depth" of a MZV, and the...

( z ) {\displaystyle \operatorname {Li} _{s}\left(z\right)} is the polylogarithm and θ ( x ) = ∫ 0 ∞ 2 t x e 2 π t − 1 sin ⁡ ( π x 2 − t ) d t {\displaystyle...

T}}\right)-1\right]}}d\lambda } This integral yields an incomplete polylogarithm function, which can make its use very cumbersome. The standard numerical...

named after Spencer Bloch and Andrei Suslin. It is closely related to polylogarithm, hyperbolic geometry and algebraic K-theory. The dilogarithm function...