Bessel function of the second kind of order 1, $Y_1(x)$.


In the Julia programming language, the function bessely1(x) calculates the Bessel function of the second kind of order 1, denoted as $Y_1(x)$.

julia> bessely1(2.5)

Here are some common examples of how to use the bessely1 function:

  1. Evaluate Bessel function for a specific value:

    julia> bessely1(2.5)

    This example calculates the value of $Y_1(2.5)$.

  2. Evaluate Bessel function for an array of values:

    julia> x = [1.0, 2.0, 3.0, 4.0];
    julia> bessely1.(x)
    4-element Array{Float64,1}:

    In this example, the bessely1 function is applied element-wise to the array x, generating an array of corresponding results.

  3. Use Bessel function in a mathematical expression:
    julia> y = bessely1(3.0);
    julia> result = exp(2 * y) + 1;

    The bessely1 function can be used within larger mathematical expressions. In this example, the value of $Y_1(3.0)$ is used in the calculation of result.

Common mistake example:

julia> bessely1(-1)
ERROR: DomainError with -1.0:
Y1 is complex for negative real arguments.

The bessely1 function produces an error when the argument is a negative real number. It is important to ensure that the input is within the valid domain of the function to avoid such errors.

See Also

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

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