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besselh

besselh(nu, k, x)

Bessel function of the third kind of order nu (Hankel function). k is either 1 or 2, selecting hankelh1 or hankelh2, respectively.

Examples

1. Compute the Hankel function of the first kind (hankelh1):

   julia> besselh(0.5, 1, 2.0)
   0.4482883573538264

   This example calculates the Hankel function of order 0.5 (nu) of the first kind (hankelh1) at x = 2.0.

2. Compute the Hankel function of the second kind (hankelh2):

   julia> besselh(2, 2, 3.5)
   -0.04656529596447402

   It computes the Hankel function of order 2 (nu) of the second kind (hankelh2) at x = 3.5.

3. Evaluate the Bessel function at multiple points:

   julia> x = [1.0, 2.0, 3.0, 4.0];
   julia> besselh(1, 1, x)
   4-element Array{Float64,1}:
   0.207115
   -0.270151
   -0.340043
   -0.409775

   In this example, the besselh function is applied to each element in the array x and returns an array of the corresponding evaluations.

Common mistake example:

julia> besselh(0, 3, 1.5)
ERROR: ArgumentError: Invalid Bessel function type, expected 1 or 2

In this example, the value of k is provided as 3, which is invalid. The second argument k should be either 1 or 2 to select hankelh1 or hankelh2 respectively. Ensure that the value of k is correctly specified to avoid such errors.

See Also

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