Fungrim symbol: Exp

Symbol: Exp —

{e}^{z}

— Exponential function

The exponential function

{e}^{z}

is a function of one complex variable

z

. It can be defined by the Taylor series 1635f5.

In rendered formulas, Exp(z) is shown as

{e}^{z}

or as

\exp\!\left(z\right)

depending on the typographical requirements; no semantic difference is implied.

Definitions:

Fungrim symbol	Notation	Short description
`Exp`	${e}^{z}$	Exponential function

Source code for this entry:

Entry(ID("dfbcd9"),
    SymbolDefinition(Exp, Exp(z), "Exponential function"),
    Description("The exponential function", Exp(z), "is a function of one complex variable", z, ".", "It can be defined by the Taylor series", EntryReference("1635f5"), "."),
    Description("In rendered formulas,", SourceForm(Exp(z)), "is shown as", Exp(z), "or as", Call(Exp, z), "depending on the typographical requirements; no semantic difference is implied."))

Topics using this symbol

The symbol Exp appears in 55 topics:

Exponential function (in 49 entries)
Series and product representations of Jacobi theta functions (in 42 entries)
Jacobi theta functions (in 24 entries)
Lambert W-function (in 20 entries)
Argument transformations for Jacobi theta functions (in 20 entries)
Eisenstein series (in 18 entries)
Lattice transformations for Jacobi theta functions (in 12 entries)
Integrals of Jacobi theta functions (in 12 entries)
Coulomb wave functions (in 12 entries)
Digamma function (in 10 entries)
Barnes G-function (in 10 entries)
Dedekind eta function (in 9 entries)
Sinc function (in 8 entries)
Error functions (in 8 entries)
Confluent hypergeometric functions (in 8 entries)
Bounds and inequalities for the gamma function (in 7 entries)
Bessel functions (in 7 entries)
Powers (in 6 entries)
Gamma function (in 6 entries)
Factorials and binomial coefficients (in 6 entries)
Dirichlet characters (in 6 entries)
Weierstrass elliptic functions (in 5 entries)
Sine (in 5 entries)
Pi (in 5 entries)
Natural logarithm (in 5 entries)
Totient function (in 4 entries)
Square roots (in 4 entries)
Modular lambda function (in 4 entries)
Hypergeometric representations of Bessel functions (in 4 entries)
Definite integrals (in 4 entries)
Bell numbers (in 4 entries)
Approximations of Jacobi theta functions (in 4 entries)
Specific values of Bessel functions (in 3 entries)
Operators (in 3 entries)
Modular j-invariant (in 3 entries)
Euler's constant (in 3 entries)
Riemann hypothesis (in 2 entries)
Partition function (in 2 entries)
Modular transformations (in 2 entries)
Legendre elliptic integrals (in 2 entries)
Imaginary unit (in 2 entries)
Hurwitz zeta function (in 2 entries)
Halphen's constant (in 2 entries)
Fibonacci numbers (in 2 entries)
Dirichlet L-functions (in 2 entries)
Complex plane (in 2 entries)
Chebyshev polynomials (in 2 entries)
Bernoulli numbers and polynomials (in 2 entries)
Arithmetic-geometric mean (in 2 entries)
Stirling numbers (in 1 entries)
Stieltjes constants (in 1 entries)
Riemann zeta function (in 1 entries)
Legendre polynomials (in 1 entries)
Complex parts (in 1 entries)
Catalan's constant (in 1 entries)

Entries using this symbol

The symbol Exp appears in 363 entries: