DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Composite trapezoidal rule

Definition

Let $a < b$ be real numbers, let $N \geq 1$ be an integer, put $h : = (b - a) / N$ , and let $x_{j} : = a + j h$ for $0 \leq j \leq N$ . For any real-valued function $f : [a, b] \to R$ , its composite trapezoidal value with $N$ equal panels is $T_{N} (f) : = h (\frac{f (x_{0})}{2} + \sum_{j = 1}^{N - 1} f (x_{j}) + \frac{f (x_{N})}{2}) .$ The sum is the finite sum of Finite sums and finite products, by recursion; when $N = 1$ it is empty and equals $0$ . This definition gives a finite real number for every such $f$ . An error comparison with $\int_{a}^{b} f$ is asserted only when that integral is defined.

Depends on

Finite sums and finite products, by recursion

Used by

Dependency tree · two levels

13 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Tobin A. Driscoll and Richard J. Braun, Fundamentals of Numerical Computation, §5.6.1–§5.6.4 (standard reference, not scraped)
Endre Süli, Numerical Computation, course notes (standard reference, not scraped)