# besselyx

besselyx(nu, x)

Scaled Bessel function of the second kind of order nu, $Y_\nu(x) e^{- | \operatorname{Im}(x) |}$.

## Examples

In the Julia programming language, the function besselyx(nu, x) calculates the scaled Bessel function of the second kind of order nu, denoted as Y_nu(x). The scaling factor used is exp(-abs(im(x))).

julia> besselyx(0, 1.5)
-0.5103756726497452

julia> besselyx(1, 2.5)
0.09148886494129613

Here are some common examples of how to use the besselyx function:

1. Calculate Y_nu(x) for specific order and argument:

julia> besselyx(2, 3.5)
0.10027615301393665

This example calculates the value of Y_2(3.5).

2. Evaluate Y_nu(x) for an array of arguments:

julia> x = [0.5, 1.0, 1.5, 2.0];
julia> besselyx(1, x)
4-element Array{Float64,1}:
-0.781212821300288
-0.781212821300288
-0.5103756726497452
0.22389077914123562

This example evaluates Y_1(x) for each element in the array x.

3. Obtain the scaled Bessel function for complex arguments:
julia> besselyx(1, 2 + 3im)
-0.21968055339661706 + 0.4657474658863984im

The besselyx function can handle complex arguments as well.

Common mistake example:

julia> besselyx(-1, 4)
ERROR: DomainError: The order of the Bessel function must be non-negative.

In this example, a negative order (-1) is provided to the besselyx function, which results in a DomainError. The order parameter (nu) must be non-negative.