Fungrim entry: 288da1

{e}^{\gamma} = \lim_{N \to \infty} \frac{1}{\log\!\left(p_{N}\right)} \prod_{n=1}^{N} \frac{p_{n}}{p_{n} - 1}

TeX:

{e}^{\gamma} = \lim_{N \to \infty} \frac{1}{\log\!\left(p_{N}\right)} \prod_{n=1}^{N} \frac{p_{n}}{p_{n} - 1}

Definitions:

Fungrim symbol	Notation	Short description
`Exp`	${e}^{z}$	Exponential function
`ConstGamma`	$\gamma$	The constant gamma (0.577...)
`SequenceLimit`	$\lim_{n \to a} f(n)$	Limiting value of sequence
`Log`	$\log(z)$	Natural logarithm
`PrimeNumber`	$p_{n}$	nth prime number
`Product`	$\prod_{n} f(n)$	Product
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("288da1"),
    Formula(Equal(Exp(ConstGamma), SequenceLimit(Mul(Div(1, Log(PrimeNumber(N))), Product(Div(PrimeNumber(n), Sub(PrimeNumber(n), 1)), For(n, 1, N))), For(N, Infinity)))))

Topics using this entry

Euler's constant

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