- 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...
-
intimately connected with the polylogarithm,
inverse tangent integral,
polygamma function,
Riemann zeta function,
Dirichlet eta function, and Dirichlet...
- 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 ) = (...
- In mathematics, the
generalized polygamma function or
balanced negapolygamma function is a
function introduced by
Olivier Espinosa Aldunate and Victor...
- The
polygamma identities can be used to
obtain a
multiplication theorem for
harmonic numbers. The
Hurwitz zeta
function generalizes the
polygamma function...
- a
qubit in a
quantum computer. Psi is also used as the
symbol for the
polygamma function,
defined by ψ ( m ) ( z ) = d m d z m Γ ′ ( z ) Γ ( z ) {\displaystyle...
- (z)} is the
gamma function. ψ n ( z ) {\displaystyle \psi _{n}(z)} is a
polygamma function. Li s ( z ) {\displaystyle \operatorname {Li} _{s}(z)} is a...
-
additional relationships can be
derived from the
Taylor series for the
polygamma function at z = 1,
which is ψ ( m ) ( z + 1 ) = ∑ k = 0 ∞ ( − 1 ) m +...
- The
derivatives of the
gamma function are
described in
terms of the
polygamma function, ψ(0)(z): Γ ′ ( z ) = Γ ( z ) ψ ( 0 ) ( z ) . {\displaystyle...
