{"id":"taylor-series","domain":"analysis","type":"Concept","title":"Taylor Series","slug":"taylor-series","url":"/mathematics/analysis/taylor-series/","summary":"Represents smooth functions as infinite polynomial sums built from derivatives. Named after Brook Taylor (1715). Underlies calculator computation of sin/cos and numerical approximation.","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Taylor, B. (1715). Methodus Incrementorum Directa et Inversa. London."},{"tier":1,"citation":"Rudin, W. (1976). Principles of Mathematical Analysis. 3rd ed."},{"tier":2,"citation":"Roy, R. (2021). Series and Products in the Development of Mathematics. 2nd ed."},{"tier":3,"citation":"Simmons, G.F. (2016). Calculus with Analytic Geometry. 2nd ed."}],"relationships":[{"type":"built_from","target":"derivative","label":"Derivative"},{"type":"uses","target":"series-and-convergence","label":"Series & Convergence"},{"type":"related_to","target":"fourier-series","label":"Fourier Series"},{"type":"precursor","target":"madhava","label":"Mādhava"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"2.4"}