Symbol D
D is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Read this term in its guide →Published equation contexts
Why this formula appears here
The Text REtrieval Conference, run annually by the U.S. National Institute of Standards and Technology from 1992 onward, gave information retrieval something the field had mostly lacked: a shared, blind evaluation on a common document set, repeated every year with published results. Robertson, Walker, and colleagues at City University London entered TREC-3 in 1994 with the Okapi system, reporting a term-weighting approach within a probabilistic relevance framework and applying it, among other extensions, to phrase weighting and to query expansion using terms drawn from an initial pilot search [ 2 ] . Over that and the following TREC rounds, the Okapi team’s tuning of term-frequency…
Read the representative guide
Symbol Q
Q appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.
Read this term in its guide →Symbol q_i
appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.
Read this term in its guide →Symbol f
the frequency of query term in D , |D| is the document’s length, is the average document length in the collection, and .
Read this term in its guide →Symbol k_1
is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Symbol b
tuned constants controlling term-frequency saturation and length normalization respectively.
Read this term in its guide →Starting index or lower bound: q_i in Q
This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.
Read this term in its guide →Numerator: f(q_i, D) × (k_1 + 1)
The complete quantity above the fraction bar.
Read this term in its guide →Denominator: f(q_i, D) + k_1 × (1 - b + b × dfrac|D|avgdl)
The complete quantity below the fraction bar; it must be nonzero for this division.
Read this term in its guide →How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.
Research cited beside this formula
Published contexts (1)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 8 · AI Agents & Systems
From BM25 to Agentic Retrieval: A History of Retrieval-Augmented Generation
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
The Text REtrieval Conference, run annually by the U.S. National Institute of Standards and Technology from 1992 onward, gave information retrieval something the field had mostly lacked: a shared, blind evaluation on a common document set, repeated every year with published results. Robertson, Walker, and colleagues at City University London entered TREC-3 in 1994 with the Okapi system, reporting a term-weighting approach within a probabilistic relevance framework and applying it, among other extensions, to phrase weighting and to query expansion using terms drawn from an initial pilot search [ 2 ] . Over that and the following TREC rounds, the Okapi team’s tuning of term-frequency…
Meanings in this article
- : the frequency of query term in D , |D| is the document’s length, is the average document length in the collection, and .
- : tuned constants controlling term-frequency saturation and length normalization respectively.