How to implement arctan function in Java?-CodePudding

Function to implement

here is the function

Code

public class arctan {
    public static double arctan(double x) {
        double sum = 0;
        int k = 0;

        double arctan1 = (Math.pow(-1, k) * (Math.pow(x, 2 * k   1) / (2 * k   1)));
        for (int i = k; i < 100; i  ) {
            sum =  arctan1;
        }
        return (double) arctan1;
    }
}

Issue

My program just gives back my x as output. I don't see the mistake I am doing.

CodePudding user response：

You have to put double arctan1 = (Math.pow(-1, k) * (Math.pow(x, 2 * k 1) / (2 * k 1))); in the loop as well since that is what the Σ is doing in the formula.

You also didn't need to have a new variable i in the for loop in this case. Using k like the formula is fine.

So it would be like this instead:

public class arctan {
    public static double arctan(double x) {
        double sum = 0;

        for (int k = 0; k < 100; i  ) {
            sum  = (Math.pow(-1, k) * (Math.pow(x, 2 * k   1) / (2 * k   1)));
        }
        return sum;
    }
}

CodePudding user response：

What does the letter Σ (sum over) mean?

See Wikipedia about the mathematical sum-symbol (uppercase sigma in Greek alphabet): Σ.

In you case it is the sum over a range from k = 0 until k = infinite.

The sum of the term following the sigma.

Define it as function instead variable

The term following is implemented correctly by: double arctan1 = (Math.pow(-1, k) * (Math.pow(x, 2 * k 1) / (2 * k 1)));

Extract it as function of k and x:

public static double arctan1(int k, double x) {
    return ( Math.pow(-1, k) * (Math.pow(x, 2 * k   1) / (2 * k   1) ));
}

Because the calculation is depending on inputs k and x now, you can use it in your sum-over range of k:

// Note: the limit is 99 here, not infinite
for (int k = 0; k < 100; k  ) {
  sum  = arctan1( k,x );  // increasing k used as input
}

Put it all together

// your "term following the sum-over" implemented by function arctan1(int k, double x)
 
public static double arctan(double x) {
    double sum = 0;
    // your loop to sum-up for increasing k
    return sum;
}