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Bessel K Function
Math Engineering Class

Public Function BesselK( _
      ByVal vX As Variant _
    , ByVal vFNU As Variant _
    ) As Variant

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

    BesselK(.5, 0) = 0.924419071227663
    BesselK(.5, 1) = 1.6564411200033
    BesselK(.5, 1.5) = 3.22514281049976
    BesselK(.5, 2) = 7.55018355124087
    BesselK(.5, 0) = BesselK0(.5)
    BesselK(.5, 1) = BesselK1(.5)
See also:
    BesselK0 Function
    BesselK0E Function
    BesselK1 Function
    BesselK1E Function
    BesselKE Function
    BesselI Function
    BesselJ Function
    BesselY 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.

BesselK 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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