Beta - Maple Help

Beta

Beta function

Calling Sequence

 Beta(x, y) $\mathrm{Β}\left(x,y\right)$

Parameters

 x - algebraic expression y - algebraic expression

Description

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

$\mathrm{Β}\left(x,y\right)=\frac{\mathrm{\Gamma }\left(x\right)\mathrm{\Gamma }\left(y\right)}{\mathrm{\Gamma }\left(x+y\right)}$

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

$\mathrm{Β}\left(x,y\right)=\underset{t\to 0}{lim}\frac{\mathrm{\Gamma }\left(x+t\right)\mathrm{\Gamma }\left(y\right)}{\mathrm{\Gamma }\left(x+t+y\right)}$

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

Examples

 > $\mathrm{Β}\left(1,2\right)$
 $\frac{{1}}{{2}}$ (1)
 > $\mathrm{Β}\left(1.2+3.4I,-2.1+5.7I\right)$
 ${0.6600944470}{-}{1.126821143}{}{I}$ (2)
 > $\mathrm{Β}\left(-\frac{3}{2},-\frac{5}{2}\right)$
 ${0}$ (3)
 > $\mathrm{NumericStatus}\left(\mathrm{invalid_operation}=\mathrm{false}\right):$
 > $\mathrm{Β}\left(-3,2\right)$
 $\frac{{1}}{{6}}$ (4)
 > $\mathrm{NumericStatus}\left(\mathrm{invalid_operation}\right)$
 ${\mathrm{true}}$ (5)