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beta(x, y) represents the beta function .
The beta function is defined for complex arguments x and y.
The result is expressed by calls to the gamma function if both
arguments are of type
Type::Numeric. Note that the beta function
may have a regular value, even if Γ(x) or Γ(y) and Γ(x + y) are
singular. In such cases
beta returns the limit
of the quotients of the singular terms.
A floating-point value is returned if both arguments are numerical and at least one of them is a floating-point value.
An unevaluated call of
beta is returned,
if none of the arguments vanishes and at least one of the arguments
does not evaluate to a number of type
When called with floating-point arguments, the function is sensitive
to the environment variable
DIGITS which determines the numerical
We demonstrate some calls with exact and symbolic input data:
beta(1, 5), beta(I, 3/2), beta(1, y + 1), beta(x, y)
Floating point values are computed for floating-point arguments:
beta(3.5, sqrt(2)), beta(sqrt(2), 2.0 + 10.0*I)
The gamma function is singular if its argument is a nonpositive
beta has a regular value
for the following arguments:
diff(beta(x^2, x), x)
expand(beta(x - 1, y + 1))
diff(beta(x, y), x); diff(beta(x, y), y);
normal(series(beta(x, y), y = 0, 3))
series(beta(x, x), x = infinity, 4)
Arithmetical expression or a floating-point interval.