**Public Function BesselKE( _
ByVal vX As Variant _
, ByVal vFNU As Variant _
) As Variant**

**Compute the exponentially scaled modified (hyperbolic) Bessel function of the third kind of order vFNU. **

**Examples:** BesselKE(.5, 0) = 1.5241093857739
BesselKE(.5, 1) = 2.73100970821179
BesselKE(.5, 1.5) = 5.31736155271655
BesselKE(.5, 2) = 12.448148218621
BesselKE(.5, 0) = BesselK0E(.5)
BesselKE(.5, 1) = BesselK1E(.5)

**See also:** BesselK0E Function
BesselK1E Function
BesselK Function
BesselIE Function
DBESK Subroutine

**vX:** Function returns Null if vX is Null or cannot be fixed up to a Double precision floating point number.

**vFNU:** Function returns Null if vFNU is Null or cannot be fixed up to a Double precision floating point number. BesselKE implements forward recursion on the three term recursion relation for a one member sequence of non-negative order Bessel functions K/sub(FNU)/(X), for real X > 0 and non-negative orders FNU. If FNU < NULIM, orders FNU and FNU+1 are obtained from DBSKNU to start the recursion. If FNU >= NULIM, the uniform asymptotic expansion is used for orders FNU and FNU+1 to start the recursion. NULIM is 35 or 70 depending on whether N=1 or N >= 2. Under and overflow tests are made on the leading term of the asymptotic expansion before any extensive computation is done.

The maximum number of significant digits obtainable is the smaller of 14 and the number of digits carried in double precision arithmetic.

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