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In the second step, the distributive law is used to simplify each of the two terms. Note that this process involves a total of three applications of the distributive property. In contrast to the FOIL method, the method using distributivity can be applied easily to products with more terms such as trinomials and higher.
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 ...
These conventions are used in combinatorics, [4] although Knuth's underline and overline notations _ and ¯ are increasingly popular. [ 2 ] [ 5 ] In the theory of special functions (in particular the hypergeometric function ) and in the standard reference work Abramowitz and Stegun , the Pochhammer symbol ( x ) n {\displaystyle (x)_{n}} is used ...
An explicit formula for the Bernoulli polynomials is given by = = [+ = () (+)]. That is similar to the series expression for the Hurwitz zeta function in the complex plane. . Indeed, there is the relationship = (,) where (,) is the Hurwitz zeta functi
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.
Differentiating by x the above formula n times, then setting x = b gives: ()! = and so the power series expansion agrees with the Taylor series. Thus a function is analytic in an open disk centered at b if and only if its Taylor series converges to the value of the function at each point of the disk.
It has order 4, because that is the smallest positive exponent that produces the identity. Below is a shear mapping with infinite order. Below that are their compositions, which both have order 3. In mathematics, an iterated function is a function that is obtained by composing another function with
Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include: