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2. Wheat and chessboard problem - Wikipedia

   en.wikipedia.org/wiki/Wheat_and_chessboard_problem

   When expressed as exponents, the geometric series is: 2 0 + 2 1 + 2 2 + 2 3 + ... and so forth, up to 2 63. The base of each exponentiation, "2", expresses the doubling at each square, while the exponents represent the position of each square (0 for the first square, 1 for the second, and so on.). The number of grains is the 64th Mersenne number.

3. Exponentiation - Wikipedia

   en.wikipedia.org/wiki/Exponentiation

   In mathematics, exponentiation, denoted b n, is an operation involving two numbers: the base, b, and the exponent or power, n. [1] When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, b n is the product of multiplying n bases: [1] = ⏟.

4. 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]

5. Series expansion - Wikipedia

   en.wikipedia.org/wiki/Series_expansion

   A Laurent series is a generalization of the Taylor series, allowing terms with negative exponents; it takes the form = and converges in an annulus. [6] In particular, a Laurent series can be used to examine the behavior of a complex function near a singularity by considering the series expansion on an annulus centered at the singularity.

6. Tetration - Wikipedia

   en.wikipedia.org/wiki/Tetration

   In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. There is no standard notation for tetration, though Knuth's up arrow notation ↑ ↑ {\displaystyle \uparrow \uparrow } and the left-exponent x b {\displaystyle {}^{x}b} are common.

7. Stretched exponential function - Wikipedia

   en.wikipedia.org/wiki/Stretched_exponential_function

   The compressed exponential function (with β > 1) has less practical importance, with the notable exception of β = 2, which gives the normal distribution. In mathematics, the stretched exponential is also known as the complementary cumulative Weibull distribution.