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Equation 8 · Part 12 · From BM25 to Agentic Retrieval: A History of Retrieval-Augmented Generation

subscript

score(D,Q)=∑qi∈QIDF(qi)⋅f(qi,D)⋅(k1+1)f(qi,D)+k1⋅(1−b+b⋅∣D∣avgdl),\mathrm{score}(D, Q) = \sum_{q_i \in Q} \mathrm{IDF}(q_i) \cdot \frac{f(q_i, D) \cdot (k_1 + 1)}{f(q_i, D) + k_1 \cdot \left(1 - b + b \cdot \dfrac{|D|}{\mathrm{avgdl}}\right)},
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

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…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.