Fungrim entry: f4750b

\operatorname{det}\!\left(H_{n}\right) = \frac{{\left(G\!\left(n + 1\right)\right)}^{4}}{G\!\left(2 n + 1\right)}

Assumptions:

n \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
`Pow`	${a}^{b}$	Power
`BarnesG`	$G(z)$	Barnes G-function
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	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

Barnes G-function

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC