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A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
A series may also be represented with capital-sigma notation: [8] ... A geometric series [20] [21] is one where each successive term is produced by multiplying the ...
The geometric series is an infinite series derived from a special type of sequence called a geometric progression.This means that it is the sum of infinitely many terms of geometric progression: starting from the initial term , and the next one being the initial term multiplied by a constant number known as the common ratio .
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
In mathematical analysis and in probability theory, a σ-algebra ("sigma algebra"; also σ-field, where the σ comes from the German "Summe" [1]) on a set X is a nonempty collection Σ of subsets of X closed under complement, countable unions, and countable intersections. The ordered pair (,) is called a measurable space.
This series can be written by using sigma notation, as in the right side formula. [1] ... The Maclaurin series of 1 / 1 − x is the geometric series
The sigma model can also be written in a more fully geometric notation, as a fiber bundle with fibers over a differentiable manifold. Given a section ϕ : M → Φ {\displaystyle \phi :M\to \Phi } , fix a point x ∈ M . {\displaystyle x\in M.}
When z is 1, the function is called the sigma function or sum-of-divisors function, [1] [3] and the subscript is often omitted, so σ(n) is the same as σ 1 (n) (OEIS: A000203). The aliquot sum s ( n ) of n is the sum of the proper divisors (that is, the divisors excluding n itself, OEIS : A001065 ), and equals σ 1 ( n ) − n ; the aliquot ...