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RJ Function
Math Engineering Class

Public Function RJ( _
      ByVal vX As Variant _
    , ByVal vY As Variant _
    , ByVal vZ As Variant _
    , ByVal vP As Variant _
    ) As Variant

Compute the incomplete or complete (X or Y or Z is zero) elliptic integral of the 3rd kind.

Examples: 
    RJ(1, 1, 3, 4) = 0.286898213878455
    RJ(1, 2, 3, 4) = 0.239848099749568
    RJ(2, 1, 3, 4) = 0.239848099749568
    RJ(2, 2, 3, 4) = 0.202320259296164
See also: 
    RC Function
    RD Function
    RF Function
    DRJ 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.
vP: Function returns Null if vP is Null or cannot be fixed up to a Double precision floating point number.

For X, Y, and Z non-negative, at most one of them zero, and P positive, RJ(X,Y,Z,P) = Integral from zero to infinity of (3/2)(t+X)^(-1/2)(t+Y)^(-1/2)(t+Z)^(-1/2)(t+P)^(-1) dt.

The routine calculates an approximation result to RJ(X,Y,Z,P) = Integral from zero to infinity of 

              -1/2     -1/2     -1/2     -1
    (3/2)(t+X)    (t+Y)    (t+Z)    (t+P)  dt,
where X, Y, and Z are nonnegative, at most one of them is zero, and P is positive. If X or Y or Z 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.

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