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...

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

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...

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

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...

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

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

{\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 =...

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 )...

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

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

(disambiguation), rivers in China and Thailand Long Island, New York Li, the polylogarithm function Li, the logarithmic integral function <li></li>, indicating...

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...

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...

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...

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...

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

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...

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

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

{\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...

( 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...

of the Riemann zeta function which generates special values of the polylogarithm function. The zeta function ξ k ( s ) {\displaystyle \xi _{k}(s)} is...

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...

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

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

n ⁡ ( 1 − p ) {\displaystyle \operatorname {Li} _{-n}(1-p)} is the polylogarithm function. The cumulant generating function of the geometric distribution...