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Fungrim entry: a62320

ψ(m) ⁣(1)=(−1)m+1m!ζ ⁣(m+1)\psi^{(m)}\!\left(1\right) = {\left(-1\right)}^{m + 1} m ! \zeta\!\left(m + 1\right)
Assumptions:m∈Z≥1m \in \mathbb{Z}_{\ge 1}
TeX:
\psi^{(m)}\!\left(1\right) = {\left(-1\right)}^{m + 1} m ! \zeta\!\left(m + 1\right)

m \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
DigammaFunctionψ ⁣(z)\psi\!\left(z\right) Digamma function
Powab{a}^{b} Power
Factorialn!n ! Factorial
RiemannZetaζ ⁣(s)\zeta\!\left(s\right) Riemann zeta function
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("a62320"),
    Formula(Equal(DigammaFunction(1, m), Mul(Mul(Pow(-1, Add(m, 1)), Factorial(m)), RiemannZeta(Add(m, 1))))),
    Variables(m),
    Assumptions(Element(m, ZZGreaterEqual(1))))

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2021-03-15 19:12:00.328586 UTC