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Comparison of Stirling's approximation with the factorial. 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 ...
The word "factorial" (originally French: factorielle) was first used in 1800 by Louis François Antoine Arbogast, [18] in the first work on Faà di Bruno's formula, [19] but referring to a more general concept of products of arithmetic progressions. The "factors" that this name refers to are the terms of the product formula for the factorial. [20]
Yates analysis. In statistics, a Yates analysis is an approach to analyzing data obtained from a designed experiment, where a factorial design has been used. Full- and fractional-factorial designs are common in designed experiments for engineering and scientific applications. In these designs, each factor is assigned two levels, typically ...
Commonly, a binomial coefficient is indexed by a pair of integers n ≥ k ≥ 0 and is written It is the coefficient of the xk term in the polynomial expansion of the binomial power (1 + x)n; this coefficient can be computed by the multiplicative formula. which using factorial notation can be compactly expressed as.
Legendre's formula. In mathematics, Legendre's formula gives an expression for the exponent of the largest power of a prime p that divides the factorial n!. It is named after Adrien-Marie Legendre. It is also sometimes known as de Polignac's formula, after Alphonse de Polignac.
Principal component analysis (PCA) is a widely used method for factor extraction, which is the first phase of EFA. [4] Factor weights are computed to extract the maximum possible variance, with successive factoring continuing until there is no further meaningful variance left. [4] The factor model must then be rotated for analysis.
Designed experiments with full factorial design (left), response surface with second-degree polynomial (right) In statistics, a full factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or "levels", and whose experimental units take on all possible combinations of these levels across all such factors.
In mathematics, the double factorial of a number n, denoted by n‼, is the product of all the positive integers up to n that have the same parity (odd or even) as n. [1] That is, Restated, this says that for even n, the double factorial [2] is while for odd n it is For example, 9‼ = 9 × 7 × 5 × 3 × 1 = 945. The zero double factorial 0‼ ...