Beta function

In mathematics, beta function denotes:

• Euler's beta function , also Euler's integral of the first kind ${\displaystyle \mathrm {B} (x,y)}$
• Dirichlet's beta function , which is related to the Riemann zeta function ${\displaystyle \beta (s)}$
• When renormalizing a quantum field theory, Symanzik's beta function describes how the coupling constant depends on the scale.
• Beta function (accelerator physics) , the transverse extension of a particle beam as a function of the longitudinal location.

This is a disambiguation page for differentiating between several terms identified with the same word.