in closed form

USAGE SUMMARY

The phrase "in closed form" is correct and usable in written English.
It is commonly used in mathematics and other formal fields to describe an equation or expression that can be written in a finite and explicit manner, without the use of infinite or abstract terms. Example: The solution to the quadratic equation can be written in closed form as x = (-b ± √(b^2-4ac))/2a.

✓ Grammatically correct

Science

Academia

Formal & Business

Human-verified examples from authoritative sources

Exact Expressions

56 human-written examples

So let's proceed to evaluate that sum in closed form.

Massachusetts Institute of Technology

"Comprehensively Stress Testing the Economy in Closed Form".

Harvard University

Moreover, the observer gains are obtained in closed form.

IFAC Proceedings Volumes

Such solution however does not exist in closed form.

Engineering Analysis with Boundary Elements

The characteristic equations are derived in closed form.

Composite Structures

Particular solutions and exact solutions in closed form are obtained.

Journal of Computational and Applied Mathematics

The element matrices are analytically integrated in closed form.

Journal of Sound and Vibration

Human-verified similar examples from authoritative sources

Similar Expressions

4 human-written examples

We show maximum likelihood estimates (MLEs) of cell probabilities can be obtained in closed-form.

Journal of the Korean Statistical Society

They are formulated in backstepping coordinates so that a solution is attainable in closed-form.

Automatica

p and n to be found in closed-form.

EURASIP Journal on Wireless Communications and Networking

Generally, the PAPR cannot be expressed in closed-form.

EURASIP Journal on Advances in Signal Processing

Expert writing Tips

Best practice

Use "in closed form" to clearly indicate that a solution is expressed with a finite number of standard operations and functions. This avoids ambiguity and clearly communicates the nature of the solution.

Common error

Avoid using "in closed form" when the solution is derived through numerical methods or approximations. The phrase specifically implies an exact, analytical solution, not an estimate.

Linguistic Context

The phrase "in closed form" functions as an adverbial phrase, modifying a verb to indicate how a solution, equation, or expression is obtained or represented. It describes the manner in which something is expressed mathematically. Ludwig examples show that the phrase is used to describe derivations, solutions, and equations.

Expression frequency: Very common

Frequent in

Science

71%

Academia

21%

Formal & Business

7%

Less common in

News & Media

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, the phrase "in closed form" is a grammatically correct and commonly used adverbial phrase, especially within scientific and academic contexts. Ludwig AI confirms its validity and appropriateness for describing exact mathematical solutions. The phrase emphasizes the direct and explicit nature of a solution, distinguishing it from approximate or iterative results. While alternatives exist, "in closed form" provides a specific and well-understood meaning in technical fields. When writing, ensure you're referring to an exact solution rather than an approximation to maintain accuracy and clarity. The primary contexts for this phrase are in Science and Academia.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

expressed explicitly

Stresses the explicit representation of the solution.

in explicit terms

Indicates that the solution is presented in a clear and unambiguous manner.

represented explicitly

Stresses that the solution has an explicit form.

explicitly formulated

Focuses on the clarity and directness of the formulation.

expressed directly

Emphasizes the directness of the solution's expression.

in an analytical form

Highlights the analytical nature of the expression.

directly solvable

Highlights the ability to find a solution without iterative methods.

analytically derived

Emphasizes the derivation through analytical methods.

with a direct solution

Focuses on the availability of a non-iterative solution.

directly computed

Focuses on the ability to compute the solution directly.

FAQs

What does "in closed form" mean mathematically?

In mathematics, "in closed form" means an expression can be written using a finite number of standard operations (like addition, subtraction, exponentiation, logarithms) and functions (like trigonometric functions), without infinite sums or limits. It represents an exact, analytical solution.

When is it appropriate to use the phrase "in closed form"?

Use "in closed form" when you want to emphasize that a solution or expression is exact and can be written explicitly using a finite number of standard mathematical operations and functions. Avoid using it for approximate or numerical solutions.

What are some alternatives to saying "in closed form"?

Depending on the context, you can use alternatives like "explicitly formulated", "directly solvable", or "analytically derived". These alternatives emphasize different aspects of having a direct and explicit solution.

How does a "closed-form" solution differ from a numerical solution?

A "closed-form" solution is an exact solution expressed with a finite number of standard mathematical operations. A numerical solution, on the other hand, is an approximate solution obtained through iterative or computational methods. A "closed-form" solution provides an exact formula, while a numerical solution provides an approximate value.