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  2. Newton's identities - Wikipedia

    en.wikipedia.org/wiki/Newton's_identities

    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.

  3. Table of Newtonian series - Wikipedia

    en.wikipedia.org/wiki/Table_of_Newtonian_series

    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) This follows from the general form of a Newton series for equidistant nodes (when it exists, i.e. is convergent)

  4. Contributions of Leonhard Euler to mathematics - Wikipedia

    en.wikipedia.org/wiki/Contributions_of_Leonhard...

    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.

  5. Binomial coefficient - Wikipedia

    en.wikipedia.org/wiki/Binomial_coefficient

    Newton's binomial series, named after Sir Isaac Newton, ... The identity can be obtained by showing that both sides satisfy the differential equation ...

  6. Sums of powers - Wikipedia

    en.wikipedia.org/wiki/Sums_of_powers

    Newton's identities express the sum of the k th powers of all the roots of a polynomial in terms of the coefficients in the polynomial. The sum of cubes of numbers in arithmetic progression is sometimes another cube. The Fermat cubic, in which the sum of three cubes equals another cube, has a general solution.

  7. De analysi per aequationes numero terminorum infinitas

    en.wikipedia.org/wiki/De_analysi_per_aequationes...

    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.

  8. Symmetric polynomial - Wikipedia

    en.wikipedia.org/wiki/Symmetric_polynomial

    The Newton identities provide an explicit method to do this; it involves division by integers up to n, which explains the rational coefficients. Because of these divisions, the mentioned statement fails in general when coefficients are taken in a field of finite characteristic ; however, it is valid with coefficients in any ring containing the ...

  9. List of mathematical identities - Wikipedia

    en.wikipedia.org/.../List_of_mathematical_identities

    Heine's identity; Hermite's identity; Lagrange's identity; Lagrange's trigonometric identities; List of logarithmic identities; MacWilliams identity; Matrix determinant lemma; Newton's identity; Parseval's identity; Pfister's sixteen-square identity; Sherman–Morrison formula; Sophie Germain identity; Sun's curious identity; Sylvester's ...