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Fungrim entry: f4750b

det ⁣(Hn)=(G ⁣(n+1))4G ⁣(2n+1)\operatorname{det}\!\left(H_{n}\right) = \frac{{\left(G\!\left(n + 1\right)\right)}^{4}}{G\!\left(2 n + 1\right)}
Assumptions:nZ0n \in \mathbb{Z}_{\ge 0}
TeX:
\operatorname{det}\!\left(H_{n}\right) = \frac{{\left(G\!\left(n + 1\right)\right)}^{4}}{G\!\left(2 n + 1\right)}

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Powab{a}^{b} Power
BarnesGG(z)G(z) Barnes G-function
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("f4750b"),
    Formula(Equal(Det(HilbertMatrix(n)), Div(Pow(BarnesG(Add(n, 1)), 4), BarnesG(Add(Mul(2, n), 1))))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(0))))

Topics using this entry

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2021-03-15 19:12:00.328586 UTC