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# What is the Y0 function in Golang?

Faraz Karim

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The programming language Go uses the Y0 function to find the order-zero Bessel function of the second kind for any argument it is passed.

To use this function, you must import the math package in your file and access the Y0 function within it using the . notation (math.Y0). Here, Y0 is the actual function, while math is the Go package that stores the definition of this function.

### The Bessel functions

The Bessel functions are canonical solutions to Bessel’s differential equation. These solutions are in the form:

$y= AJ_{v}(x) + BY_{v}(x)$

In the equation above, subscript $v$ determines the order of the functions (the Bessel functions are defined for all real values of $v$). So, for $v = 0$, the produced solutions will be of order-zero.

In the equation above, $Y$ represents the second solution to the Bessel equation, also known as the Bessel function of the second kind.

### Function definition

The definition of the Y0 function inside the math package is shown below:

### Parameters

The Y0 function takes a single argument of type float64 that represents the number for which you want to find the second kind order-zero Bessel function.

### Return value

The Y0 function returns a single value of type float64 that represents the second kind order-zero Bessel function of the given argument.

Some special cases are when you pass infinity, 0, or NAN as an argument:

• If the argument has a value of +Inf, the return value will be 0.

• If the argument has a value of 0, the return value will be -Inf.

• If the argument is a NAN value or is less than 0 (a negative value), then the return value will be NAN.

### Code

Below is a simple example where we find the second order-zero Bessel function of 5.35.

package mainimport(  "fmt"   "math") func main() {	var x float64 = 5.35 	y := math.Y0(x)	fmt.Print("The second kind order-zero Bessel function of ", x," is ", y)}

The example below shows how the Y0 function deals with an argument with a value of positive infinity.

To generate the infinite value, we use the Inf function in the math package. Inf generates an infinite value with the same sign as the argument passed to it.

package mainimport(  "fmt"   "math") func main() {	var x float64 = math.Inf(1)	y := math.Y0(x)	fmt.Print("The second kind order-zero Bessel function of ", x," is ", y, "\n")}

The example below shows how the Y0 function handles NAN values.

Here, we use the NaN function present in the math package to generate a NAN value.

package mainimport(  "fmt"   "math") func main() {  my_nan := math.NaN()	y := math.Y0(my_nan)	fmt.Print("The second kind order-zero Bessel function of ", my_nan," is ", y, "\n")}

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Faraz Karim