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  2. Factorial - Wikipedia

    en.wikipedia.org/wiki/Factorial

    For example, 9!! = 1 × 3 × 5 × 7 × 9 = 945. Double factorials are used in trigonometric integrals, [92] in expressions for the gamma function at half-integers and the volumes of hyperspheres, [93] and in counting binary trees and perfect matchings. [91] [94] Exponential factorial

  3. Double factorial - Wikipedia

    en.wikipedia.org/wiki/Double_factorial

    The factorial of a positive n may be written as the product of two double factorials: [3]! =!! ...

  4. Falling and rising factorials - Wikipedia

    en.wikipedia.org/wiki/Falling_and_rising_factorials

    An alternative notation for the rising factorial () is the less common () +. When () + is used to denote the rising factorial, the notation () is typically used for the ordinary falling factorial, to avoid confusion. [3]

  5. Factorial number system - Wikipedia

    en.wikipedia.org/wiki/Factorial_number_system

    The term "factorial number system" is used by Knuth, [3] while the French equivalent "numération factorielle" was first used in 1888. [4] The term "factoradic", which is a portmanteau of factorial and mixed radix, appears to be of more recent date.

  6. Stirling's approximation - Wikipedia

    en.wikipedia.org/wiki/Stirling's_approximation

    In mathematics, Stirling's approximation (or Stirling's formula) is an asymptotic approximation for factorials. It is a good approximation, leading to accurate results even for small values of . It is named after James Stirling, though a related but less precise result was first stated by Abraham de Moivre. [1] [2] [3]

  7. List of mathematical series - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_series

    2.3 Trigonometric, inverse trigonometric, hyperbolic, and inverse hyperbolic functions relationship 2.4 Modified-factorial denominators 2.5 Binomial coefficients

  8. Gamma function - Wikipedia

    en.wikipedia.org/wiki/Gamma_function

    In mathematics, the gamma function (represented by Γ, capital Greek letter gamma) is the most common extension of the factorial function to complex numbers.Derived by Daniel Bernoulli, the gamma function () is defined for all complex numbers except non-positive integers, and for every positive integer =, () = ()!.

  9. Factorion - Wikipedia

    en.wikipedia.org/wiki/Factorion

    For =, the sum of the factorials of the digits is simply the number of digits in the base 2 representation since ! =! =. A natural number n {\displaystyle n} is a sociable factorion if it is a periodic point for SFD b {\displaystyle \operatorname {SFD} _{b}} , where SFD b k ⁡ ( n ) = n {\displaystyle \operatorname {SFD} _{b}^{k}(n)=n} for a ...