Fungrim entry: 9f703a

Symbol: PrimeSum —

\sum_{p} f(p)

— Sum over primes

PrimeSum(f(p), For(p)), rendered as

\sum_{p} f(p)

, represents the sum of

f(p)

taken over all prime numbers

p

PrimeSum(f(p), For(p), P(p)), rendered as

\sum_{P(p)} f(p)

, represents the sum of

f(p)

taken over all prime numbers

p

satisfying the predicate

P(p)

The special expression For(p) defines p as a locally bound variable.

The empty sum is equal to zero. Sums taken over an infinite number of terms are required to be absolutely convergent.

Definitions:

Fungrim symbol	Notation	Short description
`PrimeSum`	$\sum_{p} f(p)$	Sum over primes

Source code for this entry:

Entry(ID("9f703a"),
    SymbolDefinition(PrimeSum, PrimeSum(f(p), For(p)), "Sum over primes"),
    Description(SourceForm(PrimeSum(f(p), For(p))), ", rendered as ", PrimeSum(f(p), For(p)), ", represents the sum of", f(p), "taken over all prime numbers", p, "."),
    Description(SourceForm(PrimeSum(f(p), For(p), P(p))), ", rendered as ", PrimeSum(f(p), For(p), P(p)), ", represents the sum 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 sum is equal to zero. Sums taken over an infinite number of terms are required to be absolutely convergent."))

Topics using this entry

Operators