“e”的概念、定义、翻译、参考文献-科学参考

Physics

The irrational number defined as the limit as n tends to infinity of (1+1/n)ⁿ. It has the value 2.718 28…. It is used as the base of natural logarithms and occurs in the exponential function, e^x.

Mathematics

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

$\int_{1}^{e} \frac{1}{t} d t = 1 .$

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

$e = lim_{h \to 0} {(1 + h)}^{1 / h} = lim_{n \to ∞} {(1 + \frac{1}{n})}^{n},$

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

$1 + \frac{1}{1!} + \frac{1}{2!} + \dots + \frac{1}{n!} + \dots .$

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.

Statistics

See exponential.

Chemical Engineering

The irrational number that has the value of 2.718 281 828 . . . It is calculated from (1+1/n)ⁿ where n tends to infinity. It is used as the base of natural or Naperian logarithms and exponential functions involving e^x.

单词	e
释义	e Physics The irrational number defined as the limit as n tends to infinity of (1+1/n)ⁿ. It has the value 2.718 28…. It is used as the base of natural logarithms and occurs in the exponential function, e^x. Mathematics 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 $\int_{1}^{e} \frac{1}{t} d t = 1 .$ The number e has important properties derived from some of the properties of ln and exp. For example, $e = lim_{h \to 0} {(1 + h)}^{1 / h} = lim_{n \to ∞} {(1 + \frac{1}{n})}^{n},$ which is how Jacques Bernoulli first defined the number in 1683. Also, e is the sum of the series $1 + \frac{1}{1!} + \frac{1}{2!} + \dots + \frac{1}{n!} + \dots .$ 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. Statistics See exponential. Chemical Engineering The irrational number that has the value of 2.718 281 828 . . . It is calculated from (1+1/n)ⁿ where n tends to infinity. It is used as the base of natural or Naperian logarithms and exponential functions involving e^x.
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