closed-form expression

The function T cannot be written as a closed-form expression.

This can occur, for instance, when the solution does not have a closed-form expression, or is too complicated.

The solution to the Schrödinger equation for hydrogen is closed-form expression.

After some algebraic handling, their closed-form expression can be found:

If an integer relation is found, this suggests a possible closed-form expression for the original series, product or integral.

The maximum-likelihood estimates lack a closed-form expression and must be found by numerical methods.

A closed-form expression for first-order beta wavelets can easily be derived.

Most functions do not have explicit general closed-form expressions for the n-th iterate.

A standard example of an elementary function whose antiderivative does not have a closed-form expression is:

There is no known closed-form expression of the MRB constant.

Closed-form expressions for situations where the product form condition does not hold can be computed numerically as described below in the simulation section.

Closed-form expressions for beta wavelets and scale functions as well as their spectra are derived.

A closed-form solution (or closed-form expression) is any formula that can be evaluated in a finite number of standard operations.

For example, in principle the Jordan form could give a closed-form expression for the exponential exp(A).

Certain special cases of conic optimization problems have notable closed-form expressions of their dual problems.

In 1991 a closed-form expression was developed for the equivalent depth (d) that can replace the Hooghoudt tables:

Unfortunately, there is no direct closed-form expression for the geometric median; it is typically computed using iterative methods.

If a closed-form expression is needed, the method of moments can be applied to estimate from the sample skew, by inverting the skewness equation.

A conjugate prior is an algebraic convenience, giving a closed-form expression for the posterior: otherwise a difficult numerical integration may be necessary.

In general, there is no closed-form expression for the best-fitting parameters, as there is in linear regression.

However, the class of expressions considered to be analytical expressions tends to be wider than that for closed-form expressions.

The quantile function can be expressed in a closed-form expressions using the Lambert W function:

A CIR process is a special case of a basic affine jump diffusion, which still permits a closed-form expression for bond prices.

Recurrence relations may lead to previously unknown properties of a sequence, but generally closed-form expressions for the terms of a sequence are more desired.

Methods for separately calculating the extinction from each species using closed-form expressions are described in Schaefer (1993) and Schaefer (1998).