如何用python实现泰勒展开公式

在Python中，我们可以使用循环结构和数学库`math`来实现泰勒展开公式。泰勒展开是一种近似计算技术，它将复杂函数表示为无穷级数，通常在函数在某一点处可导的条件下成立。下面是一个简单的例子，展示如何使用泰勒公式对某个函数进行n阶展开：

import math

def taylor_seriesExpansion(func, x, n, point=0):
    """
    Taylor Series Expansion function
    :param func: The target function (a callable)
    :param x: The variable value where we want to expand the series
    :param n: The order of the expansion
    :param point: The point around which to expand (default is 0)
    :return: A list containing coefficients for the Taylor series
    """
    coefficients = [func(point)]
    
    # Calculate derivatives up to n-th order
    for i in range(1, n + 1):
        derivative = math.factorial(i) * func(point + i * (x - point)) / math.pow(i, i)
        coefficients.append(derivative)

    return coefficients

# 使用示例：e^x 的泰勒展开到2阶
def exponential_function(x):
    return math.exp(x)

expansion = taylor_seriesExpansion(exponential_function, 1, 2)
print("Taylor expansion of e^x at x=1 up to 2nd order:", expansion)