Grokking Modern System Design Interview for Engineers & Managers
Ace your System Design Interview and take your career to the next level. Learn to handle the design of applications like Netflix, Quora, Facebook, Uber, and many more in a 45-min interview. Learn the RESHADED framework for architecting web-scale applications by determining requirements, constraints, and assumptions before diving into a step-by-step design process.
The programming language Go uses the Yn
function to find the order-n Bessel function of the second kind for the passed argument.
To use this function, you must import the math
package in your file and access the Yn
function within it using the .
notation (math.Yn
). Here, Yn
is the actual function, while math
is the Go package that stores the definition of this function.
The Bessel functions are canonical solutions to Bessel’s differential equation. These solutions are in the form below:
$y= AJ_{v}(x) + BY_{v}(x)$
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 $v = 1$, the solutions produced will be of order-one. For $v = 2$, it’ll be order-two, and so on.
In the equation above, $Y$ represents the second solution to the Bessel equation, also known as the Bessel function of the second kind.
The definition of the Yn
function inside the math
package is as follows:
The Yn
function takes two arguments:
n
: An argument of type int
that represents the order of the second kind Bessel function you need to find.
a
: An argument of type float64
that represents the number you want to find the second kind order-n Bessel function of.
The Yn
function returns a single value of type float64
that represents the second kind order-n Bessel function of the argument a
.
Some special cases are:
If the value of a
is +Inf, then 0 is returned.
If a
is 0 and n
is greater than 0, then -Inf is returned.
If n
is negative, then the returned value is:
+Inf
if n
is odd.-Inf
if n
is even .If the argument is NAN
or is negative, then the returned value is NAN
.
Below is a simple example where we use the Yn
function to we find out the order-0 Bessel function of the second kind for 5.35
and compare it to the return value of the Y0
function.
package mainimport("fmt""math")func main() {var x float64 = 5.35y := math.Yn(0, x)y0 := math.Y0(x)fmt.Print("Y0(",x,") = ", y0,"\n")fmt.Print("Yn(0, ",x,") = ", y)}
The example below shows how the Yn
function handles the special cases.
package mainimport("fmt""math")func main() {n := 2a:=math.Yn(1, math.Inf(1))b:=math.Yn(n , 0)c:=math.Yn((-1*n) , 0)d:=math.Yn(n, -1)e:=math.Yn(n, math.NaN())fmt.Println("Yn(0, +Inf), =" , a)fmt.Println("Yn(0, 0) = ", b)fmt.Println("Yn(0, 0) = ", c)fmt.Println("Yn(0, -1) = ", d)fmt.Println("Yn(0, NaN) = ", e)}
Here, we use the
NaN
function present in themath
package to generate aNAN
value.
To generate an infinite value, we use the
Inf
function in themath
package, which generates an infinite value with the same sign as the argument passed to it.
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Grokking Modern System Design Interview for Engineers & Managers
Ace your System Design Interview and take your career to the next level. Learn to handle the design of applications like Netflix, Quora, Facebook, Uber, and many more in a 45-min interview. Learn the RESHADED framework for architecting web-scale applications by determining requirements, constraints, and assumptions before diving into a step-by-step design process.