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 ?
Farrell and Ross present a selection of problems, each with a solution worked out in detail, dealing with the properties and applications of the Gamma function and the Beta function, the Legendre polynomials, and the Bessel functions.
1] (1, b; c; z) = [phi](b; c; z) is known as incomplete beta function.
where [beta] (l,m) is the beta function with l, m > 0 and is defined as
Integration Techniques, Gamma Function, Beta Function, Cauchy
properties of the beta function, rewrite the integral as 1.
Tables of the Incomplete Beta Function, Cambridge University Press, Cambridge, UK, first edition (1934).
GSK-3 beta function is important in a variety of biological processes, and mice with the tagged protein exhibited many problems in utero, including cleft palates and sternum defects.
The area of a spherical cap can also be described using the incomplete Beta function.
where B is the beta function and we have used the homogeneity of R to divide the variables by their arithmetic average,
where [alpha] > 0, [beta], > 0, and B([alpha], [beta]) is the beta function defined by
Changing the variable, t = 2x - 1, we get immediately the integral defining the beta function, and as a consequence
Nine appendices (about 40 pages) give background on mathematical relations, gamma and beta functions, Fourier series, basic theorems of the theory of second-order and linear second-order differential equations, perturbation methods, and discrete models of two TNL oscillations.