The

beta function In mathematics, the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial coefficients. It is defined by the integral : \Beta(z_1,z_2) = \int_0^1 t^ ...

, also called the Euler beta function or the Euler integral of the first kind, is a special function in mathematics.

Other meanings

Beta function may also refer to: *

Beta function (physics) In theoretical physics, specifically quantum field theory, a beta function or Gell-Mann–Low function, ''β(g)'', encodes the dependence of a coupling parameter, ''g'', on the energy scale, ''μ'', of a given physical process described by qu ...

, details the running of the coupling strengths *

Dirichlet beta function In mathematics, the Dirichlet beta function (also known as the Catalan beta function) is a special function, closely related to the Riemann zeta function. It is a particular Dirichlet L-function, the L-function for the alternating character of p ...

, closely related to the Riemann zeta function *

Gödel's β function In mathematical logic, Gödel's ''β'' function is a function used to permit quantification over finite sequences of natural numbers in formal theories of arithmetic. The ''β'' function is used, in particular, in showing that the class of arithmet ...

, used in mathematical logic to encode sequences of natural numbers *

Beta function (accelerator physics) The beta function in accelerator physics is a function related to the transverse size of the particle beam at the location s along the nominal beam trajectory. It is related to the transverse beam size as follows: \sigma(s) = \sqrt where * s i ...

, related to the transverse beam size at a given point in a beam transport system

Other meanings

See also