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Exponential factorial

Index Exponential factorial

The exponential factorial of a positive integer n, denoted by n$, is n raised to the power of n − 1, which in turn is raised to the power of n − 2, and so on and so forth, that is, The exponential factorial can also be defined with the recurrence relation The first few exponential factorials are 1, 1, 2, 9, 262144, etc. [1]

13 relations: Complex number, Exponentiation, Factorial, Gamma function, MathWorld, Real number, Recurrence relation, Tetration, Transcendental number, 1, 100,000, 2, 9.

Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Exponentiation

Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.

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Factorial

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, The value of 0! is 1, according to the convention for an empty product.

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Gamma function

In mathematics, the gamma function (represented by, the capital Greek alphabet letter gamma) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers.

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MathWorld

MathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Recurrence relation

In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given: each further term of the sequence or array is defined as a function of the preceding terms.

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Tetration

In mathematics, tetration (or hyper-4) is the next hyperoperation after exponentiation, and is defined as iterated exponentiation.

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Transcendental number

In mathematics, a transcendental number is a real or complex number that is not algebraic—that is, it is not a root of a nonzero polynomial equation with integer (or, equivalently, rational) coefficients.

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1

1 (one, also called unit, unity, and (multiplicative) identity) is a number, numeral, and glyph.

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100,000

100,000 (one hundred thousand) is the natural number following 99,999 and preceding 100,001.

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2

2 (two) is a number, numeral, and glyph.

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9

9 (nine) is the natural number following and preceding.

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References

[1] https://en.wikipedia.org/wiki/Exponential_factorial

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