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javarecursion
Vimzy
Vimzy

Reputation: 1975

Use recursive method that uses MacLaurin series to compute e^x

How would I write a recursive static method that uses an (n+1) term MacLaurin series to compute e^x, called e(x,n), by using the following recursive formulation: 

e(x,0)= 1 
e(x,n)= e(x,n-1) + x^n/n!, if n>0

Also, my method signature needs to use the following: 

public static double eTwo(double x, long n)

Been stuck for a while, any thoughts guys?

Upvotes: 1

Views: 2366

Answers (2)

Palle
Palle

Reputation: 12129

A version which is likely a little more efficient would be to use a loop instead of recursion, because only a single stack frame needs to be allocated:

static double eTwo(double x, long n) {
    double result = 1;
    for (long i = 1; i < n; i++) 
        result += Math.pow(x, (double) i) / (double) factorial(i);
    return result;
}

static long factorial(long n) {
    long result = 1;
    for (long i = 1; i <= n; i++) 
        result *= i;
    return result;
}

Upvotes: 0

Revolution88
Revolution88

Reputation: 698

This is simplest solution that get on my mind, did you try it?

public static double eTwo(double x, long n){
    if(n==0)
        return 1;
    else 
        return eTwo(x,n-1) + Math.pow(x, n)/factorial(n);
}

public double factorial (n){
    if(n==0)
        return 1;
    else 
        return n*factorial(n-1);
}

Upvotes: 2

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