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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 ...
The name of NASA is an acronym that expands to National Aeronautics and Space Administration.. An acronym is a type of abbreviation consisting of a phrase whose only pronounced elements are the initial letters or initial sounds of words inside that phrase.
This inline template is placed after any acronym, abbreviation or initialism that needs to be expanded. Template parameters [Edit template data] This template prefers inline formatting of parameters. Parameter Description Type Status Tag and hover text type 1 Change text. in = initialism | ab = abbreviation | (null or invalid value) = acronym Auto value String optional Month and year date The ...
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.
An alternate version of this definition allows A and B to possibly overlap and then takes their disjoint union, a mechanism that allows common elements to be separated out and therefore counted twice. The other popular definition is recursive: Let n + be the successor of n, that is the number following n in the natural numbers, so 0 + = 1, 1 + = 2.
Given a quadratic polynomial of the form + the numbers h and k may be interpreted as the Cartesian coordinates of the vertex (or stationary point) of the parabola. That is, h is the x -coordinate of the axis of symmetry (i.e. the axis of symmetry has equation x = h ), and k is the minimum value (or maximum value, if a < 0) of the quadratic ...
A candidate definition was proposed independently by several mathematicians in the 1930s. [30] The best-known variant was formalised by the mathematician Alan Turing , who defined a well-defined statement or calculation as any statement that could be expressed in terms of the initialisation parameters of a Turing machine .
The mathematical constant e can be represented in a variety of ways as a real number.Since e is an irrational number (see proof that e is irrational), it cannot be represented as the quotient of two integers, but it can be represented as a continued fraction.