## Bessel Y FunctionMath Engineering Class

```Public Function BesselY( _
ByVal vX As Variant _
, ByVal vFNU As Variant _
) As Variant```

### Compute the Bessel function of the second kind of order vFNU.

Examples:
```    BesselY(.5, 0) = -0.444518733506706
BesselY(.5, 1) = -1.47147239267024
BesselY(.5, 1.5) = -2.52146555042134
BesselY(.5, 2) = -5.44137083717426
BesselY(.5, 0) = BesselY0(.5)
BesselY(.5, 1) = BesselY1(.5)```
```    BesselY0 Function
BesselY1 Function
BesselJ Function
BesselI Function
BesselK Function
DBESY 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.

BesselY implements forward recursion on the three term recursion relation for a one member sequence of non-negative order Bessel functions Y/sub(FNU)/(X), for real X > 0 and non-negative orders FNU. If FNU < NULIM, orders FNU and FNU+1 are obtained from DBSYNU which computes by a power series for X <= 2, the K Bessel function of an imaginary argument for 2 < X <= 20 and the asymptotic expansion for X > 20.
If FNU >= NULIM, the uniform asymptotic expansion is coded in DASYJY for orders FNU and FNU+1 to start the recursion. NULIM is 70 or 100 depending on whether N=1 or N >= 2. An overflow test is 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.