Fungrim symbol: ForElement

Symbol: ForElement —

\ldots

— Generator for all the elements of a set

ForElement(x, S) declares the variable x just like For(x) and additionally tells the parent operator that

x

is to range over the elements of the set

S

. Examples: Set(Mul(2, n), ForElement(n, ZZ)) becomes

\left\{ 2 n : n \in \mathbb{Z} \right\}

. Sum(Div(1, Pow(n, 2)), ForElement(n, SetMinus(ZZ, Set(0)))) becomes

\sum_{n \in \mathbb{Z} \setminus \left\{0\right\}} \frac{1}{{n}^{2}}

Definitions:

Fungrim symbol	Notation	Short description
`ZZ`	$\mathbb{Z}$	Integers
`Sum`	$\sum_{n} f(n)$	Sum
`Pow`	${a}^{b}$	Power

Source code for this entry:

Entry(ID("978576"),
    SymbolDefinition(ForElement, Ellipsis, "Generator for all the elements of a set"),
    Description(SourceForm(ForElement(x, S)), "declares the variable", SourceForm(x), "just like", SourceForm(For(x)), "and additionally tells the parent operator", "that", x, "is to range over the elements of the set", S, ". ", "Examples: ", SourceForm(Set(Mul(2, n), ForElement(n, ZZ))), "becomes", Set(Mul(2, n), ForElement(n, ZZ)), ". ", SourceForm(Sum(Div(1, Pow(n, 2)), ForElement(n, SetMinus(ZZ, Set(0))))), "becomes", Sum(Div(1, Pow(n, 2)), ForElement(n, SetMinus(ZZ, Set(0)))), ". "))

Topics using this symbol

The symbol ForElement appears in 47 topics:

Eisenstein series (in 20 entries)
Operators (in 17 entries)
Lambert W-function (in 15 entries)
Weierstrass elliptic functions (in 12 entries)
Series representations of Carlson symmetric elliptic integrals (in 12 entries)
Sine (in 9 entries)
Sinc function (in 9 entries)
Hurwitz zeta function (in 8 entries)
Digamma function (in 8 entries)
Riemann hypothesis (in 7 entries)
Riemann zeta function (in 6 entries)
Numbers and infinities (in 6 entries)
Modular lambda function (in 6 entries)
Modular j-invariant (in 6 entries)
Legendre polynomials (in 6 entries)
Halphen's constant (in 6 entries)
General analytic functions (in 6 entries)
Complex plane (in 6 entries)
Zeros of the Riemann zeta function (in 5 entries)
Inverse tangent (in 5 entries)
Exponential function (in 5 entries)
Dirichlet L-functions (in 5 entries)
Chebyshev polynomials (in 5 entries)
Carlson symmetric elliptic integrals (in 5 entries)
Barnes G-function (in 5 entries)
Square roots (in 4 entries)
Jacobi theta functions (in 4 entries)
Dirichlet characters (in 4 entries)
Airy functions (in 4 entries)
Natural logarithm (in 3 entries)
Keiper-Li coefficients (in 3 entries)
Gaussian quadrature (in 3 entries)
Gamma function (in 3 entries)
Dedekind eta function (in 3 entries)
Bounds and inequalities for the gamma function (in 3 entries)
Totient function (in 2 entries)
Prime numbers (in 2 entries)
Symbolic expressions (in 1 entries)
Pi (in 1 entries)
Multiple zeta values (in 1 entries)
Modular transformations (in 1 entries)
Landau's function (in 1 entries)
Imaginary unit (in 1 entries)
Greatest common divisor (in 1 entries)
Golden ratio (in 1 entries)
Fibonacci numbers (in 1 entries)
Elementary logic and set theory (in 1 entries)

Entries using this symbol

The symbol ForElement appears in 233 entries: