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单词 Fraction power
释义

Fraction power

中文百科

幂 Exponentiation

(重定向自Fraction power)
y = bx对各种底数b的图像,分别为绿色的10、红色的e、蓝色的2和青色的1/2。
指数函数ez可以通过(1 + z/N)N当N趋于无穷大时的极限来定义,那幺eiπ就是(1 + iπ/N)N的极限。在这个动画中n从1取到100。(1 + iπ/N)N的值通过N重复增加在复数平面上展示,最终结果就是(1 + iπ/N)N的准确值。可以看出,随着N的增大,(1 + iπ/N)N逐渐逼近极限-1。这就是欧拉公式。
Gráfica de varias funciones potencia, función cuadrática y función cúbica.

幂运算英语:Exponentiation),又称指数运算,一种数**算,表示为b,其中,b被称为底数,而n被称为指数,其结果为b自乘n次。同样的,n^m指将n自乘m次。把n^m看作乘方的结果,叫做「n的m次幂」或「n的m次方」。

其中,n称为「底数」,m称为「指数」(写成上标)。当不能用上标时,例如在编程语言或电子邮件中,n^m通常写成n^mn**m,也可视为超运算,记为n[3]m,亦可以用高德纳箭号表示法,写成n↑m,读作“n的m次方”。 当指数为1时,通常不写出来,因为运算出的值和底数的数值一样;指数为2时,可以读作“n的平方”;指数为3时,可以读作“n的立方”。

英语百科

Exponentiation 幂

(重定向自Fraction power)
Graphs of y = bx for various bases b: base 10 (green), base e (red), base 2 (blue), and base 1/2 (cyan).  Each curve passes through the point (0, 1) because any nonzero number raised to the power of 0 is 1. At x = 1, the value of y equals the base because any number raised to the power of 1 is the number itself.
From top to bottom: x1/8, x1/4, x1/2, x1, x2, x4, x8.
The exponential function ez can be defined as the limit of (1 + z/N)N, as N approaches infinity, and thus eiπ is the limit of (1 + iπ/N)N. In this animation N takes values increasing from 1 to 100. The computation of (1 + iπ/N)N is displayed as the combined effect of N repeated multiplications in the complex plane, so that (1 + iπ/N)k, k = 0 ... N are the vertices of a polygonal path whose final, leftmost endpoint is the actual value of (1 + iπ/N)N. It can be seen that as N gets larger (1 + iπ/N)N approaches a limit of −1. Therefore, eiπ = −1, which is known as Euler's identity.

Exponentiation is a mathematical operation, written as b, involving two numbers, the base b and the exponent n. When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, b is the product of multiplying n bases:

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更新时间:2025/6/21 12:28:43