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bessely1

bessely1(x)

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

Examples

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)
-1.2904365264896353

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

1. Evaluate Bessel function for a specific value:

   julia> bessely1(2.5)
   -1.2904365264896353

   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}:
   -0.7812128213002887
   -3.7109083470919374
    0.16529365185793634
    2.1357214213567424

   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

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