# bessely

bessely(nu, x)

Bessel function of the second kind of order nu, $Y_\nu(x)$.

## Examples

In the Julia programming language, the function bessely(nu, x) computes the n-th order Bessel function of the second kind, denoted as $Y_{\nu}(x)$.

julia> bessely(0, 1.0)
0.08825696421567696
1. Compute Bessel function of the second kind:

julia> bessely(1, 2.0)
-0.20748667136010965

This example calculates the first-order Bessel function of the second kind, denoted as $Y_1(2.0)$.

2. Evaluate Bessel function for complex arguments:

julia> bessely(2, 1 + 2im)
0.16476343091190485 - 0.4292964090536087im

The bessely function can also handle complex arguments. This example evaluates the second-order Bessel function of the second kind for the complex number 1 + 2im.

3. Calculate Bessel function for arrays:

julia> x = [0.5, 1.0, 1.5];
julia> bessely(2, x)
3-element Array{Float64,1}:
-1.2190158227469677
-0.20748667136010965
0.163353455497956

The bessely function can also accept arrays as input. In this example, it computes the second-order Bessel function of the second kind for each element in the array x.

Common mistake example:

julia> bessely(1.5, 2.0)
ERROR: DomainError with -0.8996460170577619:
Order must be an integer or Rational number.

In this example, the order nu is provided as a floating-point number, which results in a DomainError. The order must be an integer or a rational number. Make sure to provide a valid order for the Bessel function.