function Beta(x: Double; y: Double): Double;
Beta function B.
| # | Name | Description |
|---|---|---|
| 1 | x | x in the Beta function definition |
| 2 | real. | |
| 3 | y | y in the Beta function definition |
| 4 | real. |
Returns: Double - beta function B for given parameters x and y.
Remarks:
The (complete) Euler beta function is defined by:
B(x,y)=integral _0^1 t^(x-1)(1-t)^(y-1) dt = (Gamma(x) Gamma(y))/(Gamma(x+y)) .
Domain: x, y real, neither a non-positive integer (poles of the Gamma function). Defined behavior: computed as sgn*exp(lnGamma(x)+lnGamma(y)-lnGamma(x+y)),
carrying the combined sign of the three Gamma factors; the function is symmetric, . When lnGamma(x+y) overflows the result is 0; when lnGamma(x) or lnGamma(y) overflows the result saturates to the signed maximum value.
See Also: Math387.IGamma