series of functions

USAGE SUMMARY

The phrase "series of functions" is correct and usable in written English.
It can be used in mathematical or programming contexts to refer to a sequence or collection of functions that are related or follow a specific pattern. Example: "In calculus, we often analyze a series of functions to understand their convergence properties."

✓ Grammatically correct

Academia

Science

News & Media

Formal & Business

Human-verified examples from authoritative sources

Exact Expressions

44 human-written examples

Covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations.

Massachusetts Institute of Technology

Three options offered, each covering fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations.

Massachusetts Institute of Technology

The Heine-Borel theorem, the Riemann integral, conditions for integrability of functions and term by term differentiation and integration of series of functions, Taylor's theorem.

Princeton University

For that purpose we have developed a series of functions to guide conceptual design exploration by providing timely evaluation of design alternatives.

Automation in Construction

ADM uses a rearranged Taylor series expansion about a function and finds a series of functions which add up to generate the required solution.

Computer Methods in Applied Mechanics and Engineering

Through the natural evolutionary process, organisms have been improving amazing mineralized materials for a series of functions using a relatively few constituent elements.

Composites Science and Technology

Human-verified similar examples from authoritative sources

Similar Expressions

16 human-written examples

The TI 3PO includes a series of function useful in scientific computations such as trigonometric functions, base conversions, logarithmic functions, logical operators, inequality functions, floor and ceiling, and exponentiation.

Cornell University

City features, such as street features, buildings and environmental areas, are organized as a series of function objects that meet the various needs of the blind.

Applied Geography

A prototype machine has been designed and made, and a series of function debugging and verification experiments have been carried out on the machine.

Chinese Journal of Aeronautics

Throughout this paper, we will call (2.5) as conjugate Fourier series of function f.

Journal of Inequalities and Applications

A complex Fourier series of function x t) is defined as x ( t ) = ∑ k = − ∞ ∞ C k e jk ω 0 t (1).

Robotics and Biomimetics

Expert writing Tips

Best practice

When using "series of functions" in mathematical contexts, ensure you clearly define the properties and relationships between the functions within the series to avoid ambiguity.

Common error

Avoid assuming that a "series of functions" automatically converges. Always verify convergence properties based on the specific functions and the conditions of the series.

Linguistic Context

The phrase "series of functions" functions primarily as a noun phrase. It refers to a collection of functions, often infinite, arranged in a specific order. Ludwig's examples illustrate its use in mathematical and computational contexts, such as discussing convergence in analysis or expansion of crack displacements.

Expression frequency: Common

Frequent in

Science

65%

Academia

30%

News & Media

5%

Less common in

Formal & Business

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, "series of functions" is a noun phrase commonly used in scientific and academic contexts to denote an ordered collection of functions. Ludwig AI confirms its grammatical correctness and prevalent use across fields like mathematics, computer science, and engineering. While alternatives like "sequence of functions" or "collection of functions" exist, the choice depends on the specific nuance you wish to convey. When employing this phrase, ensure that you clearly define the properties and relationships between the functions to avoid ambiguity and verify convergence properties, as applicable.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

sequence of functions

Replaces "series" with "sequence", emphasizing the ordered arrangement of the functions.

collection of functions

Uses "collection" instead of "series", highlighting the group aspect of the functions.

set of functions

Employs "set" to denote a mathematical grouping of functions, which might not imply a specific order.

array of functions

Substitutes "series" with "array", suggesting an ordered arrangement commonly used in programming contexts.

group of functions

Replaces "series" with "group", focusing on the collective nature of the functions.

family of functions

Uses "family" to indicate a related group of functions, implying a common characteristic or origin.

succession of functions

Replaces "series" with "succession", emphasizing the sequential nature of the functions.

progression of functions

Uses "progression" instead of "series", highlighting the ordered and potentially evolving nature of the functions.

cluster of functions

Substitutes "series" with "cluster", focusing on functions that are grouped based on similarity or shared characteristics.

compilation of functions

Employs "compilation" to refer to a collection of functions, suggesting that they've been gathered together.

FAQs

How can I use "series of functions" in a sentence?

You can use "series of functions" to describe a sequence of functions, often in mathematical analysis or programming. For example: "The course covers convergence properties of a "series of functions"."

What's a good alternative to "series of functions"?

Alternatives include "sequence of functions", "collection of functions", or "set of functions", depending on the specific context and emphasis you want to convey.

What is the difference between "series of functions" and "sequence of functions"?

While similar, "series of functions" often implies a summation or combination of the functions, while "sequence of functions" simply refers to an ordered list. The terms can be interchangeable in some contexts, but the specific nuance should guide your choice.

When is it appropriate to use "series of functions" in scientific writing?

It's appropriate when describing mathematical models, signal processing techniques, or any situation where multiple functions are used sequentially or in combination to achieve a particular result. Ensure you clearly define each function and their relationships.