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Exponentiation for a natural power is defined as iterated multiplication, which Knuth ... 2 3: 27: 7,625,597,484,987 3 3 ...
The Gelfond–Schneider constant or Hilbert number [1] is two to the power of the square root of two: . 2 √ 2 ≈ 2.665 144 142 690 225 188 650 297 249 8731.... which was proved to be a transcendental number by Rodion Kuzmin in 1930. [2]
Analogously, the inverses of tetration are often called the super-root, and the super-logarithm (In fact, all hyperoperations greater than or equal to 3 have analogous inverses); e.g., in the function =, the two inverses are the cube super-root of y and the super-logarithm base y of x.
2 Power series. Toggle Power series subsection. 2.1 Low-order polylogarithms. 2.2 Exponential function. ... 7.2 Sum of reciprocal of factorials. 7.3 Trigonometry and ...
Graphs of y = b x for various bases b: base 10, base e, base 2, base 1 / 2 . 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.
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The four 4th roots of −1, none of which are real The three 3rd roots of −1, one of which is a negative real. An n th root of a number x, where n is a positive integer, is any of the n real or complex numbers r whose nth power is x:
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