besselyx(nu, x)

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


In the Julia programming language, the function besselyx(nu, x) calculates the scaled Bessel function of the second kind of order nu, denoted as Y_nu(x). The scaling factor used is exp(-abs(im(x))).

julia> besselyx(0, 1.5)

julia> besselyx(1, 2.5)

Here are some common examples of how to use the besselyx function:

  1. Calculate Y_nu(x) for specific order and argument:

    julia> besselyx(2, 3.5)

    This example calculates the value of Y_2(3.5).

  2. Evaluate Y_nu(x) for an array of arguments:

    julia> x = [0.5, 1.0, 1.5, 2.0];
    julia> besselyx(1, x)
    4-element Array{Float64,1}:

    This example evaluates Y_1(x) for each element in the array x.

  3. Obtain the scaled Bessel function for complex arguments:
    julia> besselyx(1, 2 + 3im)
    -0.21968055339661706 + 0.4657474658863984im

    The besselyx function can handle complex arguments as well.

Common mistake example:

julia> besselyx(-1, 4)
ERROR: DomainError: The order of the Bessel function must be non-negative.

In this example, a negative order (-1) is provided to the besselyx function, which results in a DomainError. The order parameter (nu) must be non-negative.

See Also

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

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