# hankelh1

hankelh1(nu, x)

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

## Examples

The hankelh1 function in Julia calculates the Hankel function of the first kind, denoted as $H^{(1)}_{\nu}(x)$, which is a type of Bessel function. It takes two arguments: nu, representing the order of the function, and x, the input value. Here are some examples of how to use the hankelh1 function:

1. Calculate the Hankel function at a specific order and input value:

julia> hankelh1(0.5, 2.0)
0.5579365079100998

This example calculates $H^{(1)}_{0.5}(2.0)$.

2. Evaluate the Hankel function for an array of input values:

julia> x = [1.0, 2.0, 3.0, 4.0];
julia> hankelh1(1.0, x)
4-element Array{Complex{Float64},1}:
0.7651976865579667 - 0.08825696421567666im
-0.2238907791412356 + 0.6977746579640079im
-0.6626776852097376 - 0.39145636673990544im
0.1580021310640927 - 0.3817869887075492im

It evaluates the Hankel function of order 1.0 for each value in the array x.

3. Handle complex order and input values:
julia> hankelh1(1.5 + 0.5im, 1.0 + 2.0im)
0.2673296543257781 - 0.5589569017432177im

This example demonstrates the usage of complex numbers for both the order and input value.

Remember to import the SpecialFunctions module to use the hankelh1 function:

using SpecialFunctions

Note: The output values of hankelh1 are complex numbers since the Hankel function can have complex values.