Please note that the recommended version of Scilab is 2024.1.0. This page might be outdated.
See the recommended documentation of this function
beta
beta function (Euler integral of the first kind)
Syntax
z = beta(x,y)
Arguments
- x, y
2 positive real scalars, vectors or matricesof equal sizes.
- z
a real or a matrix of the same size than
x
withz(i,j) = beta(x(i,j),y(i,j))
.
Description
Computes the complete beta function :
![](/docs/6.1.0/fr_FR/beta_equation1.mml.png)
For small x
and y
(x+y ≤ 2
elementwise),
the algorithm uses the expression in function of the gamma function, else it
applies the exponential function onto the result of the
betaln
function provided with the DCDFLIB: Library of
Fortran Routines for Cumulative Distribution Functions, Inverses, and
Other Parameter (see cdfbet for more
information about DCDFLIB).
Examples
// example 1 : beta(5,2) - beta(2,5) // symmetry (must be exactly 0) beta(0.5,0.5) // exact value is pi
// example 2 : an error study based on the relation B(1,x) = 1/x // (computing 1/x must lead to only a relative error of eps_m, so // it may be used near as a reference to evaluate the error in B(1,x)) x = logspace(-8,8,20000)'; e = beta(ones(x),x) - (1)./x; er = abs(e) .* x; ind = find(er ~= 0); eps = ones(x(ind))*number_properties("eps"); clf() plot2d(x(ind),[er(ind) eps 2*eps],style=[1 2 3],logflag="ll",leg="er@eps_m@2 eps_m") xtitle("approximate relative error in computing beta(1,x)") show_window()
![](/docs/6.1.0/fr_FR/beta_1.png)
// example 3 : plotting the beta function t = linspace(0.2,10,60); X = t'*ones(t); Y = ones(t')*t; Z = beta(X,Y); clf() plot3d(t, t, Z, flag=[2 4 4], leg="x@y@z", alpha=75, theta=30) xtitle("The beta function on [0.2,10]x[0.2,10]") show_window()
![](/docs/6.1.0/fr_FR/beta_2.png)
Report an issue | ||
<< besseli | Fonctions spéciales | calerf >> |