## RD FunctionMath Engineering Class

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

### Compute the incomplete or complete elliptic integral of the 2nd kind.

Examples:
```    RD(1, 1, 3) = 0.349720080430692
RD(1, 2, 3) = 0.290460281028991
RD(2, 1, 3) = 0.290460281028991
RD(2, 2, 3) = 0.243386037818348```
```    RC Function
RF Function
RJ Function
DRD 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 and Y nonnegative, X+Y and Z positive, RD(X,Y,Z) = Integral from zero to infinity of (3/2)(t+X)^(-1/2)(t+Y)^(-1/2)(t+Z)^(-3/2) dt. If X or Y is zero, the integral is complete.

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

```              -1/2     -1/2     -3/2
(3/2)(t+X)    (t+Y)    (t+Z)    dt,```
where X and Y are nonnegative, X + Y is positive, and Z is positive. If X or Y 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.