Search results
Results From The WOW.Com Content Network
A series may also be represented with capital-sigma notation: [8] ... In general, a geometric series with initial term and common ratio , =, converges ...
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 .
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:, fix a point . The pushforward at is a map of tangent bundles
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.
In capital-sigma notation this is expressed = or = + with a n > 0 for all n. Like any series, an alternating series is a convergent series if and only if the sequence of partial sums of the series converges to a limit.
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.
In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.