## RF FunctionMath Engineering Class

```Public Function RF( _
ByVal vX As Variant _
, ByVal vY As Variant _
, ByVal vZ As Variant _
) As Variant```

### Compute the incomplete or complete elliptic integral of the 1st kind.

Examples:
```    RF(1, 1, 3) = 0.810496989476754
RF(1, 2, 3) = 0.726945935468908
RF(2, 1, 3) = 0.726945935468908
RF(2, 2, 3) = 0.658478948462408```
```    RC Function
RD Function
RJ Function
DRF Function```
vX: Function returns Null if vX is Null or cannot be fixed up to a Double precision floating point number.
vY: Function returns Null if vY is Null or cannot be fixed up to a Double precision floating point number.
vZ: Function returns Null if vZ is Null or cannot be fixed up to a Double precision floating point number.

For X, Y, and Z non-negative and at most one of them zero, RF(X,Y,Z) = Integral from zero to infinity of (1/2)(t+X)^(-1/2)(t+Y)^(-1/2)(t+Z)^(-1/2) dt. If X, Y or Z is zero, the integral is complete.

Evaluate an INCOMPLETE (or COMPLETE) ELLIPTIC INTEGRAL of the first kind.
The routine calculates an approximation result to RF(X,Y,Z) = Integral from zero to infinity of

```              -1/2     -1/2     -1/2
(1/2)(t+X)    (t+Y)    (t+Z)    dt,```
where X, Y, and Z are nonnegative and at most one of them is zero. If one of them is zero, the integral is COMPLETE. The duplication theorem is iterated until the variables are nearly equal, and the function is then expanded in Taylor series to fifth order.