The Beta(x,y) function (Beta function) is defined in general as follows:

When x+y is a non-positive integer but x and y are not, then Beta(x,y) is 0.

If x is a non-positive integer then Beta(x,y) is defined by the limit:

If y is a non-positive integer but x is not, then Beta(x,y) is defined by the symmetry relation Beta(x,y) = Beta(y,x), and the above limit is used.

In the cases above where the limit is computed and is finite - for example, when x and x+y are non-positive integers but y>0 - Maple signals the invalid_operation numeric event, allowing the user to control this singular behavior by catching the event. For more information, see numeric_events.

Note that Beta(x,y) can be represented by the following integral:

Also Beta(x,y) is related to the binomial coefficient via Beta(x,y) * binomial(x+y, x) = (x+y)/x/y.

You can enter the command Beta using either the 1-D or 2-D calling sequence. For example, Beta(1, 2) is equivalent to $\mathrm{{\rm B}}\left(1\,2\right)$.

$\mathrm{{\rm B}}\left(1\,2\right)$

$\frac{1}{2}$

$\mathrm{{\rm B}}\left(1.2+3.4\mathrm{I}\,-2.1+5.7\mathrm{I}\right)$

$0.6600944470-1.126821143\mathrm{I}$

$\mathrm{{\rm B}}\left(-\frac{3}{2}\,-\frac{5}{2}\right)$

$0$

$\mathrm{NumericStatus}\left(\mathrm{invalid\_operation}=\mathrm{false}\right)\:$

$\mathrm{{\rm B}}\left(-3\,2\right)$

$\frac{1}{6}$

$\mathrm{NumericStatus}\left(\mathrm{invalid\_operation}\right)$

$\mathrm{true}$