Beta¶

Euler beta function.

$ wo 'Beta[1, 1]'
1

Beta[a, b] is rational whenever one argument is an integer, including half-integer and other rational partners:

$ wo 'Beta[1/2, 3]'
16/15

The three-argument form is the incomplete beta function Beta[z, a, b]. It auto-evaluates to a closed form only when both a and b are integers:

$ wo 'Beta[2, 2, 3]'
2/3

For an exact non-integer parameter it stays symbolic, but any inexact argument forces numeric evaluation:

$ wo 'Beta[2, 1/2, 3]'
Beta[2, 1/2, 3]

$ wo 'N[Beta[2, 1/2, 3]]'
1.3199326582148885