Beta function - Maple Help

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Beta - Beta function

Calling Sequence

Beta(x, y)

Βx,y

Parameters

x

-

algebraic expression

y

-

algebraic expression

Description

• 

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

Βx,y=ΓxΓyΓx+y

• 

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

Βx,y=limt0Γx+tΓyΓx+t+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 Β1,2.

• 

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

Β1,2

12

(1)

Β1.2+3.4I,2.1+5.7I

0.66009444701.126821143I

(2)

Β32,52

0

(3)

NumericStatusinvalid_operation=false:

Β3,2

16

(4)

NumericStatusinvalid_operation

true

(5)

See Also

events, GAMMA, initialfunctions, NumericStatus


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