- In mathematics, the
polygamma function of
order m is a
meromorphic function on the
complex numbers C {\displaystyle \mathbb {C} }
defined as the (m +...
- \Gamma (z)={\frac {\Gamma '(z)}{\Gamma (z)}}.} It is the
first of the
polygamma functions. This
function is
strictly increasing and
strictly concave on...
- In mathematics, the
generalized polygamma function or
balanced negapolygamma function is a
function introduced by
Olivier Espinosa Aldunate and Victor...
- Euler.
There is also a
reflection formula for the
general n-th
order polygamma function ψ(n)(z), ψ ( n ) ( 1 − z ) + ( − 1 ) n + 1 ψ ( n ) ( z ) = (...
-
intimately connected with the polylogarithm,
inverse tangent integral,
polygamma function,
Riemann zeta function,
Dirichlet eta function, and Dirichlet...
- The
polygamma identities can be used to
obtain a
multiplication theorem for
harmonic numbers. The
Hurwitz zeta
function generalizes the
polygamma function...
- \zeta (s,q)=\sum _{k=0}^{\infty }(k+q)^{-s}}
Another expression using the
polygamma function is K ( z ) = exp [ ψ ( − 2 ) ( z ) + z 2 − z 2 − z 2 ln 2...
- \psi (n)} the
Chebyshev function ψ ( x ) {\displaystyle \psi (x)} the
polygamma function ψ m ( z ) {\displaystyle \psi ^{m}(z)} or its
special cases the...
- function:
Corresponding binomial coefficient analogue.
Digamma function,
Polygamma function Incomplete beta
function Incomplete gamma function K-function...
-
representation of
Dirichlet beta
function can be
formed in
terms of the
polygamma function β ( s ) = 1 2 s ∑ n = 0 ∞ ( − 1 ) n ( n + 1 2 ) s = 1 ( − 4 )...
