{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.trigonometric-series","code":"thing-q1149336","url":"https://ver.cy/models/thing/q1149336/","name":"trigonometric series","alternateNames":["Ramanujan's sum"],"kind":"thing","status":"published","version":"0.2.0-wave.1","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.REL"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"A series of the form a0/2 + sum over n of (an cos nx + bn sin nx); when coefficients come from a function by integration, it is a Fourier series, used to represent periodic functions.","purpose":"Let an agent handle trigonometric series by definition, convergence, Fourier coefficients and applications.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Sum of sines and cosines","Represents periodic functions","Convergence can be subtle","Foundation of harmonic 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it does not hold or has not been shown.","Present truncated series as exact results without stating the error.","Use signal analysis to extract private speech or data without consent."],"requiresHuman":["Relying on series approximations in safety-critical engineering."]},"ethics":{"considerations":["Errors in approximations can matter in engineering and medicine.","Signal analysis can expose private information."],"affectedParties":["Students and engineers","People whose signals are analysed"]},"owners":{"steward":"Nobody: a mathematical concept held in common.","roles":[],"masterSystems":[]},"relations":[{"target":"Q1474614","type":"parent","note":"registry parent class"},{"target":"function series","type":"related","note":"category"},{"target":"Fourier series","type":"related","note":"kind"},{"target":"harmonic analysis","type":"related","note":"field"},{"target":"Fourier transform","type":"related","note":"continuous analogue"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.trigonometric-series","Wikidata: Q1149336 (https://www.wikidata.org/wiki/Q1149336)"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["Sums of sin nx and cos nx","Fourier coefficients an and bn","Power series use powers of x instead","Written as sums of sines and cosines."]},"capabilities":{"applicability":"required","items":["compute Fourier coefficients","discuss convergence","apply to signals and heat equations","relate to Fourier transforms"]},"hazards":{"applicability":"required","items":["Assuming pointwise convergence","Gibbs phenomenon surprises"]},"interfaces":{"applicability":"required","items":["ISO 80000-2 notation"]},"context":{"applicability":"required","items":["Representing periodic functions in mathematics, physics and engineering.","Fourier series","general trigonometric series","Fourier sine and cosine 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2)","builtFrom":["models/things/publications/thing-q1149336/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-11T10:19:00Z","builder":"tools/build_cards.py@1.0.0"},"completeness":{"sections":{"classifiers":"filled","whatItIs":"filled","purpose":"filled","distinguishingFeatures":"filled","structure":"filled","agentConduct":"filled","ethics":"filled","owners":"filled","relations":"filled","interaction.identity":"filled","interaction.properties":"not-applicable","interaction.recognition":"filled","interaction.capabilities":"filled","interaction.hazards":"filled","interaction.interfaces":"filled","interaction.context":"filled","sources":"filled"},"notes":{"_gate":"Published through the thing publication gate 1.0 on 2026-10-06T19:51:53+00:00: completeness 1.00; sense: Wikidata description; 2 live sources; review by codex: pass","interaction.properties":"Plane XCT: no invented physical properties."},"score":1.0}}