Fungrim symbol: Re

Symbol: Re —

\operatorname{Re}(z)

— Real part

Domain	Codomain
$z \in \mathbb{R}$	$\operatorname{Re}(z) \in \mathbb{R}$
$z \in \mathbb{C}$	$\operatorname{Re}(z) \in \mathbb{R}$

Table data:

\left(P, Q\right)

such that

\left(P\right) \;\implies\; \left(Q\right)

Definitions:

Fungrim symbol	Notation	Short description
`Re`	$\operatorname{Re}(z)$	Real part
`RR`	$\mathbb{R}$	Real numbers
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("f5e62c"),
    SymbolDefinition(Re, Re(z), "Real part"),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(Element(z, RR), Element(Re(z), RR)), Tuple(Element(z, CC), Element(Re(z), RR)))))

Topics using this symbol

The symbol Re appears in 46 topics:

Hurwitz zeta function (in 20 entries)
Illustrations of Jacobi theta functions (in 19 entries)
Integrals of Jacobi theta functions (in 15 entries)
Dirichlet L-functions (in 14 entries)
Riemann zeta function (in 13 entries)
Digamma function (in 12 entries)
Carlson symmetric elliptic integrals (in 10 entries)
Jacobi theta functions (in 9 entries)
Barnes G-function (in 9 entries)
Coulomb wave functions (in 7 entries)
Zeros of the Riemann zeta function (in 6 entries)
Square roots (in 6 entries)
Series representations of Carlson symmetric elliptic integrals (in 6 entries)
Legendre elliptic integrals (in 6 entries)
Inverse tangent (in 6 entries)
Illustrations of Eisenstein series (in 6 entries)
Complex parts (in 6 entries)
Arithmetic-geometric mean (in 6 entries)
Specific values of Carlson symmetric elliptic integrals (in 5 entries)
Modular lambda function (in 5 entries)
Beta function (in 5 entries)
Sinc function (in 4 entries)
Riemann hypothesis (in 4 entries)
Natural logarithm (in 4 entries)
Exponential function (in 4 entries)
Weierstrass elliptic functions (in 3 entries)
Gamma function (in 3 entries)
Eisenstein series (in 3 entries)
Bessel functions (in 3 entries)
Sine (in 2 entries)
Lambert W-function (in 2 entries)
Gauss hypergeometric function (in 2 entries)
Error functions (in 2 entries)
Definite integrals (in 2 entries)
Confluent hypergeometric functions (in 2 entries)
Bounds and inequalities for the gamma function (in 2 entries)
Airy functions (in 2 entries)
Totient function (in 1 entries)
Stieltjes constants (in 1 entries)
Powers (in 1 entries)
Modular transformations (in 1 entries)
Modular j-invariant (in 1 entries)
Keiper-Li coefficients (in 1 entries)
Imaginary unit (in 1 entries)
Hypergeometric representations of Bessel functions (in 1 entries)
Dirichlet characters (in 1 entries)

Entries using this symbol

The symbol Re appears in 222 entries: