Fungrim entry: dc507f

G\!\left(\frac{3}{4}\right) = \frac{{e}^{3 / 32 + G / 4 \pi} {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{1 / 4}}{{2}^{1 / 8} {\pi}^{1 / 4} {A}^{9 / 8}}

TeX:

G\!\left(\frac{3}{4}\right) = \frac{{e}^{3 / 32 + G / 4 \pi} {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{1 / 4}}{{2}^{1 / 8} {\pi}^{1 / 4} {A}^{9 / 8}}

Definitions:

Fungrim symbol	Notation	Short description
`BarnesG`	$G(z)$	Barnes G-function
`Pow`	${a}^{b}$	Power
`ConstE`	$e$	The constant e (2.718...)
`ConstCatalan`	$G$	Catalan's constant
`Pi`	$\pi$	The constant pi (3.14...)
`Gamma`	$\Gamma(z)$	Gamma function

Source code for this entry:

Entry(ID("dc507f"),
    Formula(Equal(BarnesG(Div(3, 4)), Div(Mul(Pow(ConstE, Add(Div(3, 32), Div(ConstCatalan, Mul(4, Pi)))), Pow(Gamma(Div(1, 4)), Div(1, 4))), Mul(Mul(Pow(2, Div(1, 8)), Pow(Pi, Div(1, 4))), Pow(ConstGlaisher, Div(9, 8)))))))

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