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  2. Exponentiation - Wikipedia

    en.wikipedia.org/wiki/Exponentiation

    For positive real numbers, exponentiation to real powers can be defined in two equivalent ways, either by extending the rational powers to reals by continuity (§ Limits of rational exponents, below), or in terms of the logarithm of the base and the exponential function (§ Powers via logarithms, below).

  3. List of exponential topics - Wikipedia

    en.wikipedia.org/wiki/List_of_exponential_topics

    Approximating natural exponents (log base e) Artin–Hasse exponential; Bacterial growth; Baker–Campbell–Hausdorff formula; Cell growth; Barometric formula; Beer–Lambert law; Characterizations of the exponential function; Catenary; Compound interest; De Moivre's formula; Derivative of the exponential map; Doléans-Dade exponential ...

  4. 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

  5. Tetration - Wikipedia

    en.wikipedia.org/wiki/Tetration

    For example, x has a single (real) super-root if n is odd, and up to two if n is even. [ citation needed ] Just as with the extension of tetration to infinite heights, the super-root can be extended to n = ∞ , being well-defined if 1/ e ≤ x ≤ e .

  6. Exponential growth - Wikipedia

    en.wikipedia.org/wiki/Exponential_growth

    Growth like this is observed in real-life activity or phenomena, such as the spread of virus infection, the growth of debt due to compound interest, and the spread of viral videos. In real cases, initial exponential growth often does not last forever, instead slowing down eventually due to upper limits caused by external factors and turning ...

  7. Generating function - Wikipedia

    en.wikipedia.org/wiki/Generating_function

    In mathematics, a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series.Generating functions are often expressed in closed form (rather than as a series), by some expression involving operations on the formal series.

  8. Scientific notation - Wikipedia

    en.wikipedia.org/wiki/Scientific_notation

    Any real number can be written in the form m × 10 ^ n in many ways: for example, 350 can be written as 3.5 × 10 2 or 35 × 10 1 or 350 × 10 0. In normalized scientific notation (called "standard form" in the United Kingdom), the exponent n is chosen so that the absolute value of m remains at least one but less than ten (1 ≤ | m | < 10).

  9. Euler's formula - Wikipedia

    en.wikipedia.org/wiki/Euler's_formula

    Here φ is the angle that a line connecting the origin with a point on the unit circle makes with the positive real axis, measured counterclockwise and in radians. The original proof is based on the Taylor series expansions of the exponential function e z (where z is a complex number) and of sin x and cos x for real numbers x .

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