- 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...
- 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...
-
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...
-
Polylogarithm and
related functions:
Incomplete polylogarithm Clausen function Complete Fermi–Dirac integral, an
alternate form of the
polylogarithm....
-
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...
- {\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...
- of the
Riemann zeta
function which generates special values of the
polylogarithm function. The zeta
function ξ k ( s ) {\displaystyle \xi _{k}(s)} is...
-
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 )...
