n1faktoriaal

n1faktoriaal is a term found in some nonstandard mathematical texts and online discussions to denote a factorial‑like operation. In standard mathematics, the factorial of a non‑negative integer n is denoted n! and is defined as the product of all positive integers up to n. The term n1faktoriaal is typically used to refer to the same operation, particularly in regional or informal contexts, rather than as a widely adopted notation.

Definition and basic properties

For a non‑negative integer n, n1faktoriaal(n) is defined as the product of the integers from 1 to n: n1faktoriaal(n) = ∏_{k=1}^{n} k = n!. The base case is n1faktoriaal(0) = 1, and for n ≥ 1 the function satisfies the recurrence n1faktoriaal(n) = n × n1faktoriaal(n−1). For negative integers, the standard factorial is not defined, and discussions of n1faktoriaal typically restrict to non‑negative integers unless extended by other means.

Extensions and relations

In many contexts, factorials are extended to non‑integers via the gamma function, with Γ(n+1) = n! for integers n. If a text uses n1faktoriaal in a similar spirit, it may be understood to align with the generalized factorial concept where appropriate. The factorial and its variants underpin combinatorics (counting permutations and arrangements), probability, and series expansions.

See also

Factorial, double factorial, gamma function, combinatorics, permutations.