Infinite sum of positive and negative powers of a formal variable
This article needs editing to comply with Wikipedia's Manual of Style. In particular, it has problems with MOS:BBB. Please help improve the content.(July 2023) (Learn how and when to remove this message)
In mathematics, a formal distribution is an infinite sum of powers of a formal variable, usually denoted in the theory of formal distributions. The coefficients of these infinite sums can be many different mathematical structures, such as vector spaces or rings, but in applications most often take values in an algebra over a field. These infinite sums are allowed to have infinitely many positive and negative powers, and are not required to converge, and so do not define functions of the formal variable. Rather, they are interpreted as distributions, that is, linear functionals on an appropriate space of test functions. They are closely related to formal Laurent series, but are not required to have finitely many negative powers. In particular, this means even if the coefficients are ring-valued, it is not necessarily possible to multiply two formal distributions.
They are important in the study of vertex operator algebras, since the vertex operator playing a central role in the theory takes values in a space of endomorphism-valued formal distributions.[1]
^Kac, Victor G. (1998). Vertex algebras for beginners (2nd ed.). Providence, R.I.: American Mathematical Society. p. 17. ISBN 082181396X.
and 24 Related for: Formal distribution information
a formaldistribution is an infinite sum of powers of a formal variable, usually denoted z {\displaystyle z} in the theory of formaldistributions. The...
there is no unambiguous way to assign formal charges. The formal charge is a tool for estimating the distribution of electric charge within a molecule...
statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution of a random variable which...
probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] or (0, 1) in...
of the other random variable(s). In the formal mathematical setup of measure theory, the joint distribution is given by the pushforward measure, by the...
towards the line, then the distribution of the point where the ball hits the line is a Cauchy distribution. More formally, consider a point at ( x 0 ...
discrete distribution of a random variable that can take on only one fixed value; in other words, it is a deterministic distribution. Expressed formally, the...
beta distribution, hence its alternative name of multivariate beta distribution (MBD). Dirichlet distributions are commonly used as prior distributions in...
Orcinus orca and its range (in blue) In biogeography, a cosmopolitan distribution is the range of a taxon that extends across all of (or most of) the world...
than a reference value. The empirical distribution function is a formal direct estimate of the cumulative distribution function for which simple statistical...
statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional...
probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of failures in a sequence...
and Germany, StudioCanal does not have a formaldistribution unit per se, instead relying on other distribution studios and home video distributors to handle...
Government to provide support and funding, the lack of a formal and effective indigenous film distribution infrastructure and the increase in the cost of production...
for many other Linux distributions, most notably the first versions of SUSE Linux distributions, and is the oldest distribution that is still maintained...
to the increase in the number of quality films produced and more formaldistribution methods. Profitability of a film studio is crucially dependent on...
A ratio distribution (also known as a quotient distribution) is a probability distribution constructed as the distribution of the ratio of random variables...
compound probability distribution. The construction of such distributions has a formal similarity to that of mixture distributions, with either infinite...
any matter of fact. Thereafter, the minister makes replies. There is no formal motion before the house nor voting. Members may raise discussions on matters...
various forms. Formal education occurs within a structured institutional framework, such as public schools, following a curriculum. Non-formal education also...
normal distributions can be applicable to many problems involving other types of distributions. This theorem has seen many changes during the formal development...
(DDS-XTypes), 1.0, formal/2012-11-10, November 2012, http://www.omg.org/spec/DDS-XTypes/1.0/PDF UML Profile for Data Distribution, version: 1.0, http://www...
statistics, the generalized extreme value (GEV) distribution is a family of continuous probability distributions developed within extreme value theory to combine...
categorical distribution (also called a generalized Bernoulli distribution, multinoulli distribution) is a discrete probability distribution that describes...
Global Information
