Previous Page Next Page Contents

beta -- the beta function

Introduction

beta(x, y) represents the beta function gamma(x)*gamma(y)/gamma(x+y).

Call(s)

beta(x, y)

Parameters

x, y - arithmetical expressions

Returns

an arithmetical expression.

Overloadable:

x

Side Effects

When called with floating point arguments, the function is sensitive to the environment variable DIGITS which determines the numerical working precision.

Related Functions

gamma, psi

Details

Example 1

We demonstrate some calls with exact and symbolic input data:

>> beta(1, 5), beta(I, 3/2), beta(1, y + 1), beta(x, y)
                         1/2
                       PI    gamma(I)     1
                 1/5, ----------------, -----, beta(x, y)
                      2 gamma(3/2 + I)  y + 1

Floating point values are computed for floating point arguments:

>> beta(3.5, sqrt(2)), beta(sqrt(2), 2.0 + 10.0*I)
              0.1395855454, - 0.01112350756 - 0.03108193098 I

Example 2

The gamma function is singular if its argument is a nonpositive integer. Nevertheless, beta has a regular value for the following arguments:

>> beta(-3, 2)
                                    1/6

Example 3

The functions diff, expand and float handle expressions involving beta:

>> diff(beta(x^2, x), x)
                 2                     2             2
        beta(x, x ) (psi(x) + 2 x psi(x ) - psi(x + x ) (2 x + 1))
>> expand(beta(x - 1, y + 1))
                           y gamma(x) gamma(y)
                           --------------------
                           gamma(x + y) (x - 1)
>> float(beta(100, 1000))
                             7.730325902e-147

Changes




Do you have questions or comments?


Copyright © SciFace Software GmbH & Co. KG 2000