exponential function wikipedia - EAS
- The exponential function is a mathematical function denoted by or (where the argument x is written as an exponent). Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.
Domain: C, {\displaystyle \mathbb {C} }Fields of application: Pure and applied mathematicsGeneral definition: exp, , z, =, e, z, {\displaystyle \exp z=e^{z}}Motivation of invention: Analytic proofsen.wikipedia.org/wiki/Exponential_function - 大家還會問
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檢視所有 Wikipediahttps://en.wikipedia.org/wiki/Exponential_functionThe exponential function is a mathematical function denoted by or (where the argument x is written as an exponent). Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical … 查看更多內容
The exponential function is sometimes called the natural exponential function for distinguishing it from the other exponential functions. The study of any exponential function can … 查看更多內容
The exponential function arises whenever a quantity grows or decays at a rate proportional to its current value. One such situation is continuously compounded interest, and in fact it was this observation that led Jacob Bernoulli in 1683 to the number 查看更多內容
As in the real case, the exponential function can be defined on the complex plane in several equivalent forms. The most common definition of the complex exponential function parallels the power series definition for real arguments, where the real variable … 查看更多內容
The real exponential function can be characterized in a variety of equivalent ways. It is commonly defined by the following power series:
Since the 查看更多內容The importance of the exponential function in mathematics and the sciences stems mainly from its property as the unique function which is equal to its derivative and is equal to 1 … 查看更多內容
A continued fraction for e can be obtained via an identity of Euler:
The following generalized continued fraction for … 查看更多內容CC-BY-SA 授權下的維基百科文字指数函数 - 维基百科，自由的百科全书
https://zh.wikipedia.org/wiki/指数函数指数函数（英語：Exponential function）是形式為的數學函数，其中是底數（或稱基數，base），而是指數（index / exponent）。
現今指數函數通常特指以為底數的指數函數（即），為数学中重要的函数，也可寫作。这里的是数学常数，也就是自然对数函数的底数，近似值为，又称为欧拉数。Wikipedia · CC-BY-SA 授權下的文字- 預估閱讀時間: 9 分鐘
- https://simple.wikipedia.org/wiki/Exponential_function
In mathematics, the exponential function is a function that grows quicker and quicker. More precisely, it is the function , where e is Euler's constant, an irrational number that is …
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- https://en.wikipedia.org/wiki/Characterizations_of_the_exponential_function
- The six most common definitions of the exponential function exp(x) = ex for real xare: 1. Define ex by the limit e x = lim n → ∞ ( 1 + x n ) n . {\displaystyle e^{x}=\lim _{n\to \infty }\left(1+{\frac {x}{n}}\right)^{n}.} 2. Define ex as the value of the infinite series e x = ∑ n = 0 ∞ x n n ! = 1 + x + x 2 2 ! + x 3 3 ! + x 4 4 ! + ⋯ {\displaystyl...
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- https://en.wikipedia.org/wiki/Exponentiation
Exponentiation is a mathematical operation, written as b n, involving two numbers, the base b and the exponent or power n, and pronounced as "b (raised) to the (power of) n ". [1] When n is a …
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- https://en.wikipedia.org/wiki/Stretched_exponential_function
In physics, the stretched exponential function is often used as a phenomenological description of relaxation in disordered systems. It was first introduced by Rudolf Kohlrausch in 1854 to …
- https://en.wikipedia.org/wiki/List_of_integrals_of_exponential_functions
List of integrals of exponential functions - Wikipedia List of integrals of exponential functions The following is a list of integrals of exponential functions. For a complete list of integral …
- https://en.wikipedia.org/wiki/Double_exponential_function
A double exponential function (red curve) compared to a single exponential function (blue curve). A double exponential function is a constant raised to the power of an exponential …
- https://en.wikipedia.org/wiki/Exponential_growth
Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is …
- https://en.wikipedia.org/wiki/Exponential_distribution
In probability theory and statistics, the exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur …
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