# 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.