- 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...
- 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...
-
intimately connected with the polylogarithm,
inverse tangent integral,
polygamma function,
Riemann zeta function,
Dirichlet eta function, and Dirichlet...
- \zeta (s,z)}{\partial s}}\right|_{s=a}.}
Another expression using the
polygamma function is K(z)=exp[ψ(−2)(z)+z2−z2−z2ln2π]{\displaystyle K(z)=\exp...
- \Gamma (z)} is the
gamma function. ψn(z){\displaystyle \psi _{n}(z)} is a
polygamma function. Lis(z){\displaystyle \operatorname {Li} _{s}(z)} is a polylogarithm...
- 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...
- \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...
- The
polygamma identities can be used to
obtain a
multiplication theorem for
harmonic numbers. For the
Hurwitz zeta
function generalizes the
polygamma function...
