In this work, we continue that line of investigation considering the incomplete
beta function [B.sub.z](a, b).
The
Beta function B(a,b) of two variables is defined by
where B(z; s, w) is the incomplete
beta function which is equal to
Then the
beta function for the coupling constant is derived.
No doubt the classical
beta function B([alpha], [beta]) is one of the most fundamental special functions, because of its precious role in several field of sciences such as mathematical, physical, and statistical sciences and engineering.
[??](z) is closed using a presumed shape with a
Beta function as follows [20]:
Using
beta function for (13), the inner integral reduces to
with the best possible constant factor B([lambda]/2, [lambda]/2) ([lambda] > 0, B(u, v) is the
beta function) (see [18]).
To the observed data, a version of the
beta function used by WANG & ENGEL (1998), called WE model, with f(T) ranging from 0 to 1, was fitted.
B ([alpha], [beta]) denotes the
beta function and the parameters above are all positive real numbers.