# besseljx

besseljx(nu, x)

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

## Examples

In the Julia programming language, the function besseljx(nu, x) calculates the n-scaled Bessel function of the first kind of order nu, denoted as J_ν(x)e^(-|Im(x)|).

julia> besseljx(0, 2.5)
0.5986833273183378

Here are some common examples of how to use this function:

1. Calculate Bessel function for a specific order and real argument:

julia> besseljx(2, 3.5)
0.21776523893496017

This example calculates the Bessel function of order 2 (ν = 2) for a real argument x = 3.5.

2. Evaluate Bessel function for complex arguments:

julia> besseljx(1, 1 + 2im)
-0.22740742820168596 + 0.31466908128728334im

In this case, the Bessel function is evaluated for a complex argument x = 1 + 2im and order ν = 1.

3. Calculate Bessel function for an array of arguments:
julia> x = [0.5, 1.5, 2.5];
julia> besseljx(0, x)
3-element Array{Float64,1}:
0.9384698072408127
0.5118256300570327
0.5986833273183378

This example demonstrates the calculation of the Bessel function for an array of real arguments x with a fixed order ν = 0.

Common mistake example:

julia> besseljx(-1, 2)
ERROR: DomainError with -1.0:
Order of Bessel function must be non-negative integer or real.

In this example, the order -1 provided to the besseljx function is not valid. The order must be a non-negative integer or real value.