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Fungrim entry: 5830eb

Symbol: DivisorProduct knf(k)\prod_{k \mid n} f(k) Product over divisors
DivisorProduct(f(k), For(k, n)), rendered as knf(k)\prod_{k \mid n} f(k), represents the product of f(k)f(k) taken over all positive integers kk dividing the integer nn.
DivisorProduct(f(k), For(k, n), P(k)), rendered as kn,P(k)f(k)\prod_{k \mid n,\, P(k)} f(k), represents the product of f(k)f(k) taken over all positive integers kk dividing the integer nn and satisfying the predicate P(k)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
DivisorProductknf(k)\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."))

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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