“e”的概念、定义、习题解题方法及翻译-数学辞典

单词

释义

The number that is the base of natural logarithms. There are several ways of defining it. For example, define ln as in the entry the logarithmic function. Then define exp as the inverse function of ln (see exponential function). Then define e as equal to exp 1. This amounts to saying that e is the number such that

The number e has important properties derived from some of the properties of ln and exp. For example,

which is how Jacques Bernoulli first defined the number in 1683. Also, e is the sum of the series

The value of e is 2.718 281 83 (to 8 decimal places). The proof that e is irrational is comparatively easy. In 1873, Hermite proved that e is transcendental.

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