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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 ...
A stronger notion is polynomial expansion, meaning that the function f used to bound the edge density of shallow minors is a polynomial.If a hereditary graph family obeys a separator theorem, stating that any n-vertex graph in the family can be split into pieces with at most n/2 vertices by the removal of O(n c) vertices for some constant c < 1, then that family necessarily has polynomial ...
Printable version; In other projects Wikidata item; Appearance. ... Pochhammer polynomial, ascending factorial, [1] rising sequential product, or upper factorial) ...
In mathematics and computer science, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation.Although named after William George Horner, this method is much older, as it has been attributed to Joseph-Louis Lagrange by Horner himself, and can be traced back many hundreds of years to Chinese and Persian mathematicians. [1]
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point.
Plot of the Chebyshev polynomial of the first kind () with = in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D. The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as () and ().