# hankelh1x

hankelh1x(nu, x)

Scaled Bessel function of the third kind of order nu, $H^{(1)}_\nu(x) e^{-x i}$.

## Examples

In the Julia programming language, the function hankelh1x(nu, x) calculates the nScaled Bessel function of the third kind of order nu denoted as $H^{(1)}_{\nu}(x)e^{-xi}$.

Here are some examples of how to use the hankelh1x function:

1. Calculate the Hankel function for real values:

julia> hankelh1x(0.5, 2.0)
-0.17613903404806057 - 0.2748849064104399im

This example calculates the Hankel function of order 0.5 for the real value 2.0.

2. Evaluate the Hankel function for complex values:

julia> hankelh1x(1.0+2.0im, 1.0+1.0im)
-0.10344058524659211 + 0.3273439936928648im

In this example, the Hankel function is evaluated for a complex order (1.0+2.0im) and a complex argument (1.0+1.0im).

3. Calculate the Hankel function for an array of values:
julia> x = [0.5, 1.0, 1.5];
julia> hankelh1x(1.5, x)
3-element Array{ComplexF64,1}:
-0.09145318648717459 - 0.2060544684058787im
-0.10344058524659211 + 0.3273439936928648im
-0.09145318648717459 + 0.5611210533689928im

This example demonstrates how to calculate the Hankel function for an array of values using a specific order.

Please note that the returned values are complex numbers since hankelh1x deals with complex functions.

Make sure to provide appropriate values for the order nu and the argument x when using the hankelh1x function.