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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]
An alternative version uses the fact that the Poisson distribution converges to a normal distribution by the Central Limit Theorem. [5]Since the Poisson distribution with parameter converges to a normal distribution with mean and variance , their density functions will be approximately the same:
Gauss proved [7] [non-primary source needed] that = (,) = {() =,, where p represents an odd prime and a positive integer. That is, the product of the positive integers less than m and relatively prime to m is one less than a multiple of m when m is equal to 4, or a power of an odd prime, or twice a power of an odd prime; otherwise, the product ...
In this formula and in many other places, the falling factorial () in the calculus of finite differences plays the role of in differential calculus. Note for instance the similarity of Δ ( x ) n = n ( x ) n − 1 {\displaystyle \Delta (x)_{n}=n(x)_{n-1}} to d d x x n = n x n − 1 {\displaystyle {\frac {\textrm {d}}{{\textrm {d}}x}}x^{n}=nx^{n ...
Two problems where the factor theorem is commonly applied are those of factoring a polynomial and finding the roots of a polynomial equation; it is a direct consequence of the theorem that these problems are essentially equivalent.
Levy also points out that some dogs are always going to be colder than others. Small, short-haired, older, or less energetic dogs are more sensitive.
This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here, is taken to have the value
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