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  2. Exponentiation - Wikipedia

    en.wikipedia.org/wiki/Exponentiation

    In mathematics, exponentiation, denoted b n, is an operation involving two numbers: the base, b, and the exponent or power, n. [1] When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, b n is the product of multiplying n bases: [1] = ⏟.

  3. Polynomial expansion - Wikipedia

    en.wikipedia.org/wiki/Polynomial_expansion

    In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. Expansion of a polynomial expression can be obtained by repeatedly replacing subexpressions that multiply two other subexpressions, at least one of which is an addition, by the equivalent sum of products, continuing until the expression becomes a ...

  4. Trinomial expansion - Wikipedia

    en.wikipedia.org/wiki/Trinomial_expansion

    Layers of Pascal's pyramid derived from coefficients in an upside-down ternary plot of the terms in the expansions of the powers of a trinomial – the number of terms is clearly a triangular number. In mathematics, a trinomial expansion is the expansion of a power of a sum of three terms into monomials. The expansion is given by

  5. Coin problem - Wikipedia

    en.wikipedia.org/wiki/Coin_problem

    The expanded polynomial will contain powers of greater than the Frobenius number for some exponent (when GCD=1), e.g., for (+ +) the set is {6, 7} which has a Frobenius number of 29, so a term with will never appear for any value of but some value of will give terms having any power of greater than 29.

  6. Ordinal arithmetic - Wikipedia

    en.wikipedia.org/wiki/Ordinal_arithmetic

    In other words, every ordinal number α can be uniquely written as + + +, where k is a natural number, and … are ordinal numbers. Another variation of the Cantor normal form is the "base δ expansion", where ω is replaced by any ordinal δ > 1 , and the numbers c i are nonzero ordinals less than δ .

  7. 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.

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