bibkey: nist2026trigonometricseries authors: NIST Digital Library of Mathematical Functions year: 2026 title: Maclaurin Series for Trigonometric Functions doi: null url: https://dlmf.nist.gov/4.19 claim: The entire cosine series and the identity 1-cos(z)=2 sin(z/2)^2. strata_touched: [] license: citation-only triage: anchor

Maclaurin Series for Trigonometric Functions

The cosine power series and the half-angle identity are classical. Substituting z=sqrt(t) gives the entire series sum_k (-1)^k t^k/(2k)!; subtracting its constant term and dividing by t yields an entire squared-sinc profile.

SincSquareDerivativeBudget uses the pinned Mathlib cosine and hyperbolic-cosine series. Its positive integral recurrence controls all derivatives on the nonnegative half-line. The factorial budget is established by that recurrence, rather than asserted as a consequence of the profile’s name.

Verified locator

NIST Digital Library of Mathematical Functions, Version 1.2.8, released 2026-09-15, Section 4.19: https://dlmf.nist.gov/4.19.