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

Operators