Fungrim symbol: Conjugate

Symbol: Conjugate —

\overline{z}

— Complex conjugate

Domain	Codomain
$z \in \mathbb{R}$	$\overline{z} \in \mathbb{R}$
$z \in \mathbb{C}$	$\overline{z} \in \mathbb{C}$

Table data:

\left(P, Q\right)

such that

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

Definitions:

Fungrim symbol	Notation	Short description
`Conjugate`	$\overline{z}$	Complex conjugate
`RR`	$\mathbb{R}$	Real numbers
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("da5d5e"),
    SymbolDefinition(Conjugate, Conjugate(z), "Complex conjugate"),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(Element(z, RR), Element(Conjugate(z), RR)), Tuple(Element(z, CC), Element(Conjugate(z), CC)))))

Topics using this symbol

The symbol Conjugate appears in 25 topics:

Complex parts (in 6 entries)
Specific values of Carlson symmetric elliptic integrals (in 5 entries)
Dirichlet L-functions (in 5 entries)
Barnes G-function (in 3 entries)
Riemann zeta function (in 2 entries)
Legendre elliptic integrals (in 2 entries)
Dirichlet characters (in 2 entries)
Digamma function (in 2 entries)
Zeros of the Riemann zeta function (in 1 entries)
Square roots (in 1 entries)
Sine (in 1 entries)
Sinc function (in 1 entries)
Natural logarithm (in 1 entries)
Legendre polynomials (in 1 entries)
Lattice transformations for Jacobi theta functions (in 1 entries)
Lambert W-function (in 1 entries)
Jacobi theta functions (in 1 entries)
Inverse tangent (in 1 entries)
Imaginary unit (in 1 entries)
Hurwitz zeta function (in 1 entries)
Gauss hypergeometric function (in 1 entries)
Gamma function (in 1 entries)
Exponential function (in 1 entries)
Arithmetic-geometric mean (in 1 entries)
Argument transformations for Jacobi theta functions (in 1 entries)

Entries using this symbol

The symbol Conjugate appears in 41 entries: