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2. Exponential function - Wikipedia

   en.wikipedia.org/wiki/Exponential_function

   Exponential functions with bases 2 and 1/2. In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. . The exponential of a variable ⁠ ⁠ is denoted ⁠ ⁡ ⁠ or ⁠ ⁠, with the two notations used interchangeab

3. Characterizations of the exponential function - Wikipedia

   en.wikipedia.org/wiki/Characterizations_of_the...

   In mathematics, the exponential function can be characterized in many ways. This article presents some common characterizations, discusses why each makes sense, and proves that they are all equivalent. The exponential function occurs naturally in many branches of mathematics. Walter Rudin called it "the most important function in mathematics". [1]

4. Exponentiation - Wikipedia

   en.wikipedia.org/wiki/Exponentiation

   The definition of e x as the exponential function allows defining b x for every positive real numbers b, in terms of exponential and logarithm function. Specifically, the fact that the natural logarithm ln(x) is the inverse of the exponential function e x means that one has = ⁡ (⁡) = ⁡ for every b > 0.

5. E-function - Wikipedia

   en.wikipedia.org/wiki/E-function

   The exponential function is an E-function, in its case c n = 1 for all of the n. If λ is an algebraic number then the Bessel function J λ is an E-function. The sum or product of two E-functions is an E-function. In particular E-functions form a ring. If a is an algebraic number and f(x) is an E-function then f(ax) will be an E-function.

6. Euler's formula - Wikipedia

   en.wikipedia.org/wiki/Euler's_formula

   The helix is formed by plotting points for various values of and is determined by both the cosine and sine components of the formula. One curve represents the real component ( cos ⁡ θ {\displaystyle \cos \theta } ) of the formula, while another curve, rotated 90 degrees around the z-axis (due to multiplication by i {\displaystyle i ...

7. e (mathematical constant) - Wikipedia

   en.wikipedia.org/wiki/E_(mathematical_constant)

   The number e is a mathematical constant approximately equal to 2.71828 that is the base of the natural logarithm and exponential function.It is sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant, a different constant typically denoted .

8. Generating function - Wikipedia

   en.wikipedia.org/wiki/Generating_function

   There are various types of generating functions, including ordinary generating functions, exponential generating functions, Lambert series, Bell series, and Dirichlet series. Every sequence in principle has a generating function of each type (except that Lambert and Dirichlet series require indices to start at 1 rather than 0), but the ease ...

9. List of exponential topics - Wikipedia

   en.wikipedia.org/wiki/List_of_exponential_topics

   Exponential (disambiguation) Exponential backoff; Exponential decay; Exponential dichotomy; Exponential discounting; Exponential diophantine equation; Exponential dispersion model; Exponential distribution; Exponential error; Exponential factorial; Exponential family; Exponential field; Exponential formula; Exponential function; Exponential ...