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Fungrim entry: 90b26f

ψ(m) ⁣(n)=(1)m+1m!ζ ⁣(m+1,n)\psi^{(m)}\!\left(n\right) = {\left(-1\right)}^{m + 1} m ! \zeta\!\left(m + 1, n\right)
Assumptions:nZ1  and  mZ1n \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; m \in \mathbb{Z}_{\ge 1}
\psi^{(m)}\!\left(n\right) = {\left(-1\right)}^{m + 1} m ! \zeta\!\left(m + 1, n\right)

n \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; m \in \mathbb{Z}_{\ge 1}
Fungrim symbol Notation Short description
DigammaFunctionψ ⁣(z)\psi\!\left(z\right) Digamma function
Powab{a}^{b} Power
Factorialn!n ! Factorial
HurwitzZetaζ ⁣(s,a)\zeta\!\left(s, a\right) Hurwitz zeta function
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
    Formula(Equal(DigammaFunction(n, m), Mul(Mul(Pow(-1, Add(m, 1)), Factorial(m)), HurwitzZeta(Add(m, 1), n)))),
    Variables(n, m),
    Assumptions(And(Element(n, ZZGreaterEqual(1)), Element(m, ZZGreaterEqual(1)))))

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2021-03-15 19:12:00.328586 UTC