Another form for this same compound distribution, written more compactly in terms of the beta function, " B ", is as follows:
42.
Similarly the normalizing factor for the prior probability, the beta function B ( ?Prior, ?Prior ) cancels out and it is immaterial to the final result.
43.
A key property of the Beta function is its relationship to the Gamma function; proof is given below in the section on relationship between gamma function and beta function
44.
A key property of the Beta function is its relationship to the Gamma function; proof is given below in the section on relationship between gamma function and beta function
45.
*PM : alternate integral representation of beta function, id = 9481 new !-- WP guess : alternate integral representation of beta function-- Status:
46.
*PM : alternate integral representation of beta function, id = 9481 new !-- WP guess : alternate integral representation of beta function-- Status:
47.
Classical scale invariance, however, normally does not imply quantum scale invariance, because of the renormalization group involved see the discussion of the beta function below.
48.
This means that, in this limit, the beta function has a minus sign driving the behavior of the running coupling toward even smaller values as the energy increases.
49.
Comparison between different LAD functions with in-situ measurements show that, two-parameter functions ( especially Beta function ) may perform better than one-parameter functions.
50.
In 1973, it was discovered that a theory of interacting colored quarks, called quantum chromodynamics had a " "'negative beta function " " '.
