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  2. Polynomial expansion - Wikipedia

    en.wikipedia.org/wiki/Polynomial_expansion

    Instead of multiplications, the expansion steps could also involve replacing powers of a sum of terms by the equivalent expression obtained from the binomial formula; this is a shortened form of what would happen if the power were treated as a repeated multiplication, and expanded repeatedly. It is customary to reintroduce powers in the final ...

  3. Trinomial expansion - Wikipedia

    en.wikipedia.org/wiki/Trinomial_expansion

    This formula is a special case of the multinomial formula for m = 3. ... The number of terms of an expanded trinomial is the triangular number + = (+) (+) ...

  4. Binomial theorem - Wikipedia

    en.wikipedia.org/wiki/Binomial_theorem

    In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, the power ⁠ (+) ⁠ expands into a polynomial with terms of the form ⁠ ⁠, where the exponents ⁠ ⁠ and ⁠ ⁠ are nonnegative integers satisfying ⁠ + = ⁠ and the coefficient ⁠ ⁠ of each term is a specific positive integer ...

  5. Mathematical formulation of the Standard Model - Wikipedia

    en.wikipedia.org/wiki/Mathematical_formulation...

    The full expanded form of the Standard Model Lagrangian. We can now give some more detail about the aforementioned free and interaction terms appearing in the Standard Model Lagrangian density. Any such term must be both gauge and reference-frame invariant, otherwise the laws of physics would depend on an arbitrary choice or the frame of an ...

  6. Series expansion - Wikipedia

    en.wikipedia.org/wiki/Series_expansion

    A Laurent series is a generalization of the Taylor series, allowing terms with negative exponents; it takes the form = and converges in an annulus. [6] In particular, a Laurent series can be used to examine the behavior of a complex function near a singularity by considering the series expansion on an annulus centered at the singularity.

  7. Newton's identities - Wikipedia

    en.wikipedia.org/wiki/Newton's_identities

    Note that the use of determinants makes that the formula for has additional minus signs compared to the one for , while the situation for the expanded form given earlier is opposite. As remarked in (Littlewood 1950, p.

  8. Vieta's formulas - Wikipedia

    en.wikipedia.org/wiki/Vieta's_formulas

    Vieta's formulas are frequently used with polynomials with coefficients in any integral domain R.Then, the quotients / belong to the field of fractions of R (and possibly are in R itself if happens to be invertible in R) and the roots are taken in an algebraically closed extension.

  9. Generating function transformation - Wikipedia

    en.wikipedia.org/wiki/Generating_function...

    which are particularly useful in the cases where the component sequence generating functions, (), can be expanded in a Laurent series, or fractional series, in , such as in the special case where all of the component generating functions are rational, which leads to an algebraic form of the corresponding diagonal generating function.