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Abraham de Moivre FRS (French pronunciation: [abʁaam də mwavʁ]; 26 May 1667 – 27 November 1754) was a French mathematician known for de Moivre's formula, a formula that links complex numbers and trigonometry, and for his work on the normal distribution and probability theory.
The theorem appeared in the second edition of The Doctrine of Chances by Abraham de Moivre, published in 1738. Although de Moivre did not use the term "Bernoulli trials", he wrote about the probability distribution of the number of times "heads" appears when a coin is tossed 3600 times. [1] This is one derivation of the particular Gaussian ...
Abraham de Moivre originally discovered this type of integral in 1733, while Gauss published the precise integral in 1809, [1] attributing its discovery to Laplace. The integral has a wide range of applications. For example, with a slight change of variables it is used to compute the normalizing constant of the normal distribution.
In mathematics, de Moivre's formula (also known as de Moivre's theorem and de Moivre's identity) states that for any real number x and integer n it is the case that ( + ) = + , where i is the imaginary unit (i 2 = −1).
De Moivre's most notable achievement in probability was the discovery of the first instance of central limit theorem, by which he was able to approximate the binomial distribution with the normal distribution. [16] To achieve this De Moivre developed an asymptotic sequence for the factorial function —- which we now refer to as Stirling's ...
The formula was first discovered by Abraham de Moivre [2] in the form ! [] +. De Moivre gave an approximate rational-number expression for the natural logarithm of the constant. Stirling's contribution consisted of showing that the constant is precisely 2 π {\displaystyle {\sqrt {2\pi }}} .
Stirling's formula was first discovered by Abraham de Moivre in his `The Doctrine of Chances' (with a constant identified later by Stirling) in order to be used in probability theory. Several probabilistic proofs of Stirling's formula (and related results) were found in the 20th century. [4] [5]
de Moivre's illustration of his piecewise linear approximation. De Moivre's law first appeared in his 1725 Annuities upon Lives, the earliest known example of an actuarial textbook. [6] Despite the name now given to it, de Moivre himself did not consider his law (he called it a "hypothesis") to be a true description of the pattern of human ...