# Fungrim entry: 2a896d

Symbol: PrimeProduct $\prod_{p} f(p)$ Product over primes
PrimeProduct(f(p), For(p)), rendered as $\prod_{p} f(p)$, represents the product of $f(p)$ taken over all prime numbers $p$.
PrimeProduct(f(p), For(p), P(p)), rendered as $\prod_{P(p)} f(p)$, represents the product of $f(p)$ taken over all prime numbers $p$ satisfying the predicate $P(p)$.
The special expression For(p) defines p as a locally bound variable.
The empty product is equal to one. Products taken over an infinite number of factors are required to be absolutely convergent.
Definitions:
Fungrim symbol Notation Short description
PrimeProduct$\prod_{p} f(p)$ Product over primes
Source code for this entry:
Entry(ID("2a896d"),
SymbolDefinition(PrimeProduct, PrimeProduct(f(p), For(p)), "Product over primes"),
Description(SourceForm(PrimeProduct(f(p), For(p))), ", rendered as ", PrimeProduct(f(p), For(p)), ", represents the product of", f(p), "taken over all prime numbers", p, "."),
Description(SourceForm(PrimeProduct(f(p), For(p), P(p))), ", rendered as ", PrimeProduct(f(p), For(p), P(p)), ", represents the product of", f(p), "taken over all prime numbers", p, "satisfying the predicate", P(p), "."),
Description("The special expression", SourceForm(For(p)), "defines", SourceForm(p), "as a locally bound variable."),
Description("The empty product is equal to one. Products taken over an infinite number of factors are required to be absolutely convergent."))

## Topics using this entry

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

2020-08-27 09:56:25.682319 UTC