DivisorProduct(f(k), For(k, n)), rendered as ∏k∣nf(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 ∏k∣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 | ∏k∣nf(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."))