使用 MacLaurin 系列用 Java 递归计算 e^x [英] Recursively calculate e^x with Java using MacLaurin Series

问题描述

我需要编写一个递归的java方法，该方法将使用签名计算名为e(x,n)的e^x，

I need to write a recursive java method that will compute e^x called e(x,n) with the signature,

public static double eThree(double x, long n) 

并且它必须使用 MacLaurin 级数来计算 e^x，这是以下观察:

and it must use the MacLaurin series to compute e^x, which is the following observation:

1 + x(1 + x/2( 1 + x/3(1 + x/4(1 + ... ))))
e(x,0)= 1 A call to this would return a result of 1

在之前的一些帮助下，我能够制作一个不需要这种格式的文件，但我不确定要使用上述格式需要编写什么代码.谢谢大家，非常感谢您提供的任何帮助！

With some help earlier, I was able to make one that didn't require this format, but I'm not sure what I would code in order to use the format above. Thanks guys, really appreciate any help that will be given!

推荐答案

这对您有用吗?我相信它实现了算法，但它不会产生 x^n.

Does this work for you? I believe it implements the algorithm but it does not produce x^n.

public static double eThree(double x, long n) {
    return eThree(x, n, 1);
}

private static double eThree(double x, long n, int div) {
    double d = 1;
    if (n > 0) {
        d = d + (x / div) * (eThree(x, n - 1, div + 1));
    }
    return d;
}

似乎认为:

2^0 = 1.0
2^1 = 3.0
2^2 = 5.0
2^3 = 6.333333333333333
2^4 = 7.0
2^5 = 7.266666666666667
2^6 = 7.355555555555555
2^7 = 7.3809523809523805
2^8 = 7.387301587301588
2^9 = 7.388712522045855

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