In mathematics, an expression or equation is in closed form if it is formed with constants, variables, and a set of functions considered as basic and connected...

Closed form may refer to: Closed-form expression, a finitary expression Closed differential form, a differential form α {\displaystyle \alpha } whose...

recurrence with constant coefficients, the Fibonacci numbers have a closed-form expression. It has become known as Binet's formula, named after French mathematician...

trivially, by swapping 0s for 1s and shifting the positions by one. A closed form expression for the so-called rabbit sequence: The nth digit of the word is...

algebraic expression is one that is not rational, such as √x + 4. Algebraic function Analytical expression Closed-form expression Expression (mathematics)...

{\displaystyle \sum _{k=1}^{\infty }(-1)^{k}k^{1/k}.} There is no known closed-form expression of the MRB constant, nor is it known whether the MRB constant is...

numerical approximation or a closed-form expression of the roots of a univariate polynomial, i.e., determining approximate or closed form solutions of x {\displaystyle...

is no closed-form expression for the perimeter of an ellipse. Throughout history, a large number of closed-form approximations and of expressions in terms...

In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation. Other ways of solving quadratic...

on the closed form expression for this " J 3 {\displaystyle J_{3}\,} perturbation". With the "modern theory" this explicit closed form expression is not...

Czech electrical engineer and Holocaust survivor who developed a closed-form expression for the distribution factor of a symmetrical three-phase stator...

recurrences, one can express the general term of the sequence as a closed-form expression of n {\displaystyle n} . As well, linear recurrences with polynomial...

many cases these sequences have simple, closed form expressions or have a generating function with a simple form. The following rules are notable: The sequence...

2^{t/245000-t/75000}} Unfortunately there is no closed-form expression for the age, t, but it is easily found using equation solving algorithms...

may be determined without computing them exactly. Often when a closed-form expression for the solutions is not available, solutions may be approximated...

the exact same expression. For instance, the formal expressions "2" and "1+1" are not equal. Analytic expression Closed-form expression Formal calculation...

estimated by maximum-likelihood estimation (MLE). This does not have a closed-form expression, unlike linear least squares; see § Model fitting. Logistic regression...

speed). The defining integral of arc length does not always have a closed-form expression, and numerical integration may be used instead to obtain numerical...

functions of a generalized chi-squared variable do not have simple closed-form expressions. But there exist several methods to compute them numerically: Ruben's...

distribution above, which is one of the few distributions where a closed-form expression can be found (others include the uniform, the Weibull, the Tukey...

Liouville's theorem) Algebraic function – Mathematical function Closed-form expression – Mathematical formula involving a given set of operations Differential...

five partitions 1 + 1 + 1 + 1, 1 + 1 + 2, 1 + 3, 2 + 2, and 4. No closed-form expression for the partition function is known, but it has both asymptotic...

problem. Maximum-likelihood training can be done by evaluating a closed-form expression (simply by counting observations in each group),: 718  rather than...

Liouvillian functions. Algebraic function – Mathematical function Closed-form expression – Mathematical formula involving a given set of operations Derivative –...

(defined with ellipses or Σ notation), it is a common problem to find closed-form expressions for the result. For example, ∑ i = 1 n i = n ( n + 1 ) 2 . {\displaystyle...

r {\displaystyle r} is constructible if and only if there is a closed-form expression for r {\displaystyle r} using only integers and the operations for...

difficult task, and the resulting expressions may be quite laborious to obtain. For example, the closed-form expression for the THDF of the sawtooth wave...

years (Denmark, 2006). The quantile function can be expressed in a closed-form expression using the Lambert W function: Q ( u ) = α β λ − 1 λ ln ⁡ ( 1 − u...

\theta )} . A conjugate prior is an algebraic convenience, giving a closed-form expression for the posterior; otherwise, numerical integration may be necessary...

kernel F n ( x ) {\displaystyle F_{n}(x)} may also be written in a closed form expression as follows F n ( x ) = 1 n ( sin ⁡ ( n x 2 ) sin ⁡ ( x 2 ) ) 2 =...