# Fungrim entry: 5830eb

Symbol: DivisorProduct $\prod_{k \mid n} f(k)$ Product over divisors
DivisorProduct(f(k), For(k, n)), rendered as $\prod_{k \mid n} f(k)$, represents the product of $f(k)$ taken over all positive integers $k$ dividing the integer $n$.
DivisorProduct(f(k), For(k, n), P(k)), rendered as $\prod_{k \mid n,\, P(k)} f(k)$, represents the product of $f(k)$ taken over all positive integers $k$ dividing the integer $n$ and satisfying the predicate $P(k)$.
The special expression For(k, n) defines k as a locally bound variable.
The empty product is equal to one.
Definitions:
Fungrim symbol Notation Short description
DivisorProduct$\prod_{k \mid n} f(k)$ Product over divisors
Source code for this entry:
Entry(ID("5830eb"),
SymbolDefinition(DivisorProduct, DivisorProduct(f(k), For(k, n)), "Product over divisors"),
Description(SourceForm(DivisorProduct(f(k), For(k, n))), ", rendered as ", DivisorProduct(f(k), For(k, n)), ", represents the product of", f(k), "taken over all positive integers", k, "dividing the integer", n, "."),
Description(SourceForm(DivisorProduct(f(k), For(k, n), P(k))), ", rendered as ", DivisorProduct(f(k), For(k, n), P(k)), ", represents the product of", f(k), "taken over all positive integers", k, "dividing the integer", n, "and satisfying the predicate", P(k), "."),
Description("The special expression", SourceForm(For(k, n)), "defines", SourceForm(k), "as a locally bound variable."),
Description("The empty product is equal to one."))

## Topics using this entry

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

2020-01-31 18:09:28.494564 UTC