hankelh1(nu, x)

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


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)

    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.

See Also

besselh, besseli, besselix, besselj, besselj0, besselj1, besseljx, besselk, besselkx, bessely, bessely0, bessely1, besselyx, hankelh1, hankelh1x, hankelh2, hankelh2x,

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