beta function


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beta function

[′bād·ə ‚fənk·shən]
(mathematics)
A function of two positive variables, defined by
References in periodicals archive ?
By expanding the beta function, Equation (10) can be further simplified:
In this work, we continue that line of investigation considering the incomplete beta function [B.sub.z](a, b).
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.
One year later, Euler introduced the beta function defined for a pair of complex numbers a and b with positive real parts, through the integral