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

At all points (x,y) where x and y are positive integers, the above definition is equivalent to:

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

In the case that x is a non-positive integer, Beta(x,y) is defined by this limit. If y is a non-positive integer, by the symmetry relation Beta(x,y) = Beta(y,x), the above limit is used. When this limit is not finite, for example, in some cases where exactly two of the expressions x, y, and x+y are non-positive integers, 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.

$\mathrm{\Β}\left(1\,2\right)$

$\frac{1}{2}$

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

$0.6600944470-1.126821143\mathrm{I}$

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

$0$

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

$\mathrm{\Β}\left(-3\,2\right)$

$\frac{1}{6}$

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

$\mathrm{true}$