double sums

USAGE SUMMARY

The phrase "double sums" is correct and usable in written English.
It can be used in mathematical contexts, particularly when referring to the summation of two separate sums or when discussing concepts in calculus or algebra. Example: "To solve the problem, we need to calculate the double sums of the two series involved."

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

16 human-written examples

replacing double limits of independent double sums by single limit of dependent double sums.  .

Advances in Difference Equations

replacing rectangular area by triangular one; replacing double limits of independent double sums by single limit of dependent double sums.

Advances in Difference Equations

Note that in practice, the double sums in Equations 3 and 4 are finite.

Earth, Planets and Space

This triangular double integral is defined by single limit of double sums of triangularly divided areas.

Advances in Difference Equations

The antisymmetric double integral here introduced demands only single limit of double sums of triangularly divided areas.

Advances in Difference Equations

Furthermore, the sum of triangular areas is modified to be the sum of a triangular area and double sums as follows.

Advances in Difference Equations

Human-verified similar examples from authoritative sources

Similar Expressions

44 human-written examples

Reversing the double sum of (A.11) and using [10, equation (8.352.4 ], we obtain (A.2).

EURASIP Journal on Wireless Communications and Networking

Each term of the double sum of Eq. 10 corresponds to a different degree n k, where n k is a real number.

Earth, Planets and Space

When the number of earthquakes is very large, the computing takes substantially long time due to the double sum in the first term of the log likelihood (8).

Earth, Planets and Space

If the linearization formula of (P_n(x)) is available then we can compute (A_{i,j}) coefficients in Eq. (3) by using one sum instead of using double sum in Eq. (4).

Mathematical Sciences

It reads (11 with (12)where δ denotes Dirac's delta function, e r, e ϑ and e φ are unit vectors of the spherical coordinate system, and is a short expression for the double sum in Eq. (9).

Earth, Planets and Space

Expert writing Tips

Best practice

When using "double sums" in mathematical writing, ensure that the indices and limits of summation are clearly defined to avoid ambiguity.

Common error

Avoid using ambiguous or undefined index notations in "double sums". Always specify the range and variable of each summation clearly to prevent misinterpretation.

Linguistic Context

The phrase "double sums" primarily functions as a mathematical noun phrase. Ludwig AI indicates it is usable in English and often appears in contexts involving summations, series, or integrals. It refers to the sum of a sum, typically involving two indices.

Expression frequency: Common

Frequent in

Science

75%

News & Media

15%

Formal & Business

5%

Less common in

Wiki

5%

Reference

0%

Social Media

0%

Ludwig's WRAP-UP

In summary, the phrase "double sums" is a mathematically-inclined expression denoting the summation of a sum, often appearing in scientific and academic contexts. Ludwig AI confirms its grammatical correctness and usability, with example sentences showing its prevalence in mathematical analysis, physics, and computer science. While alternatives like "iterated sums" or "nested sums" exist, "double sums" is a direct and widely understood term. When using this phrase, ensure clarity in index notation to avoid ambiguity. Given its frequency in scientific literature, it's a valuable term for anyone working with complex mathematical operations.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

iterated sums

Focuses on the iterative nature of the summation.

repeated summations

Emphasizes the repetition of the summation operation.

nested sums

Highlights the nested structure of the summations.

multiple summations

General term for more than one summation.

sum of sums

Directly describes the operation being performed.

twofold summations

Specifies that there are two summations involved.

sums of pairs

Describes the summing of paired elements.

bivariate summations

Uses a statistical term to refer to summations involving two variables.

cumulative totals of sums

Highlights the cumulative aspect of summing sums.

aggregate sums

Refers to sums that are combined or totalled together.

FAQs

How to use "double sums" in a mathematical context?

Use "double sums" to express the summation of a sum, often involving two indices. For example, you might use it to calculate the total of elements in a matrix or a two-dimensional array.

What are some alternatives to using the phrase "double sums"?

Alternatives include "iterated sums", "repeated summations", or "nested sums", depending on the specific nuance you wish to convey.

In what contexts is the term "double sums" commonly used?

The term "double sums" is frequently used in mathematical analysis, physics, and computer science, particularly when dealing with series, integrals, or algorithms involving multiple iterations.

How do I correctly notate "double sums" in an equation?

Ensure that you use appropriate summation notation with clear indices and limits. For instance, ∑ᵢ ∑ⱼ aᵢⱼ represents the "double sums" of elements aᵢⱼ over indices i and j.