java - Java 中无需内置函数即可计算 e^x

Question

我是 Java 初学者，目前正在阅读《如何像计算机科学家一样思考》初学者书籍。我在迭代章节中遇到了一个问题。谁能指出我正确的方向吗？

当我使用 math.exp 时，我得到的答案与我的代码获得的答案完全不同。 请注意，这不是作业。

问题是:

One way to calculate e^x is to use the infinite series expansion e^x = 1 + x + x² /2! + x³/3! + x⁴/4! +... If the loop variable is named i, then the ith term is xⁱ/i!.

1. Write a method called myexp that adds up the first n terms of this series.

所以这是代码:

public class InfiniteExpansion {
    public static void main(String[] args){

        Scanner infinite = new Scanner(System.in);
        System.out.println("what is the  value of X?");
        double x = infinite.nextDouble();
        System.out.println("what is the power?");
        int power = infinite.nextInt();



        System.out.println(Math.exp(power));//for comparison

        System.out.println("the final value of series is: "+myExp(x, power));
    }

    public static double myExp(double myX, double myPower){

        double firstResult = myX;
        double denom = 1;
        double sum =myX;

        for(int count =1;count<myPower;count++){

            firstResult = firstResult*myX;//handles the numerator

            denom = denom*(denom+1);//handles the denominator

            firstResult = firstResult/denom;//handles the segment

            sum =sum+firstResult;// adds up the different segments
        }

        return (sum+1);//gets the final result
    }

}

Answer 1

赋值 denom = denom*(denom+1) 将给出如下序列:1, 1*2=2, 2*3=6, 6*7 =42, 42*43=... 但你想要denom = denom*count。

一般来说，我们只想打印以 1! 开头的前 n 个阶乘:1!, 2!, 3!, ... ，n!。在第 k 项，我们取第 k-1 项并乘以 k。这将是对前一项递归计算k!。具体示例:4! 是 3! 乘以 4，6! 是 5! 乘以 6。

在代码中，我们有

var n = 7;
var a = 1;
for (int i = 1; i <= n; i++ ) {
    a = a*i; // Here's the recursion mentioned above.
    System.out.println(i+'! is '+a);
}

尝试运行上面的代码并进行比较，看看运行以下代码会得到什么:

var n = 7;
var a = 1;
for (int i = 1; i <= n; i++ ) {
    a = a*(a+1);
    System.out.println('Is '+i+'! equal to '+a+'?');
}