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Newton's inequalities; Symmetric function; Fluid solutions, an article giving an application of Newton's identities to computing the characteristic polynomial of the Einstein tensor in the case of a perfect fluid, and similar articles on other types of exact solutions in general relativity.
Euler proved Newton's identities, Fermat's little theorem, Fermat's theorem on sums of two squares, and made distinct contributions to the Lagrange's four-square theorem. He also invented the totient function φ(n) which assigns to a positive integer n the number of positive integers less than n and coprime to n.
Newton's formula is of interest because it is the straightforward and natural differences-version of Taylor's polynomial. Taylor's polynomial tells where a function will go, based on its y value, and its derivatives (its rate of change, and the rate of change of its rate of change, etc.) at one particular x value.
The series does not converge, the identity holds formally. Another identity is = = = (+) (), which converges for >. This follows from the general form of a Newton series for equidistant nodes (when it exists, i.e. is convergent)
Sir Isaac Newton (25 December 1642 – 20 March 1726/27 [a]) was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author who was described in his time as a natural philosopher. [5]
Composed in 1669, [4] during the mid-part of that year probably, [5] from ideas Newton had acquired during the period 1665–1666. [4] Newton wrote And whatever the common Analysis performs by Means of Equations of a finite number of Terms (provided that can be done) this new method can always perform the same by means of infinite Equations.
In the history of physics, hypotheses non fingo (Latin for "I frame no hypotheses", or "I contrive no hypotheses") is a phrase used by Isaac Newton in the essay General Scholium, which was appended to the second edition of Philosophiae Naturalis Principia Mathematica in 1713.
This article lists mathematical identities, that is, identically true relations holding in mathematics. Bézout's identity (despite its usual name, it is not, properly speaking, an identity) Binet-cauchy identity