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This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here, is taken to have the value
The asymptotic growth of the coefficients of this generating function can then be sought via the finding of A, B, α, β, and r to describe the generating function, as above. Similar asymptotic analysis is possible for exponential generating functions; with an exponential generating function, it is a n / n!
Inflation answers this question by postulating that all the regions come from an earlier era with a big vacuum energy, or cosmological constant. A space with a cosmological constant is qualitatively different: instead of moving outward, the cosmological horizon stays put. For any one observer, the distance to the cosmological horizon is ...
Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
This can be expressed by saying that f̂ is an entire function which is rapidly decreasing in σ (for fixed τ) and of exponential growth in τ (uniformly in σ). [35] (If f is not smooth, but only L 2, the statement still holds provided n = 0. [36]) The space of such functions of a complex variable is called the Paley—Wiener space.
When the direction of a Euclidean vector is represented by an angle , this is the angle determined by the free vector (starting at the origin) and the positive -unit vector. The same concept may also be applied to lines in a Euclidean space, where the angle is that determined by a parallel to the given line through the origin and the positive x ...
The Taylor series of any polynomial is the polynomial itself.. The Maclaurin series of 1 / 1 − x is the geometric series + + + +. So, by substituting x for 1 − x, the Taylor series of 1 / x at a = 1 is
One way to avoid giving attention to growth might be extending from the economic concept of growth, which proponents of both growth and degrowth commonly adopt, to a broader concept of growth that allows for the observation of growth in other sociological characteristics of society. A corresponding "recoding" of "growth-obsessed", capitalist ...