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### IMSL_BETA

IMSL_BETA

The IMSL_BETA function evaluates the real beta function β(X, Y).

The beta function, β(x, y), is defined as:

requiring that X > 0 and Y > 0. It underflows for large parameters.

## Example

Plot the beta function over [ε, 1/4 + ε] x [ε, 1/4 + ε] for ε = 0.01. The results are shown in the Real Beta Function Plot after the code example.

`x = 1e-2 + .25 * FINDGEN(25)/24 y = x`
`b = FLTARR(25, 25)`
`FOR i = 0, 24 DO b(i, *) = IMSL_BETA(x(i), y)`
`; Compute values of the beta function.`
`SURFACE, b, x, y, XTitle = 'X', YTitle = 'Y', Az = 320, ZAxis = 2`
`; Plot the computed values as a surface and rotate the plot.`

## Errors

MATH_BETA_UNDERFLOW: Parameters must not be so large that the result underflows.

### Fatal Errors

MATH_ZERO_ARG_OVERFLOW: One of the parameters is so close to zero that the result overflows.

## Syntax

Result = IMSL_BETA(X, Y [, /DOUBLE])

## Return Value

The value of the beta function β(x, y). If no result can be computed, then NaN (Not a Number) is returned.

## Arguments

### X

First beta parameter. It must be positive.

### Y

Second beta parameter. It must be positive.

## Keywords

### DOUBLE (optional)

If present and nonzero, double precision is used.

## Version History

 6.4 Introduced