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Fungrim entry: 2a896d

Symbol: PrimeProduct pf(p)\prod_{p} f(p) Product over primes
PrimeProduct(f(p), For(p)), rendered as pf(p)\prod_{p} f(p), represents the product of f(p)f(p) taken over all prime numbers pp.
PrimeProduct(f(p), For(p), P(p)), rendered as P(p)f(p)\prod_{P(p)} f(p), represents the product of f(p)f(p) taken over all prime numbers pp satisfying the predicate P(p)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
PrimeProductpf(p)\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."))

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2020-08-27 09:56:25.682319 UTC