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Ratios of Adjacent Normalized Remainders of tan²x under Finite-Block Coefficient Perturbations
This version is not peer-reviewed. Submitted: 14 September 2026 Posted: 15 September 2026 You are already at the latest version Consider ratios of adjacent normalized Maclaurin remainders after perturbing a finite block of consecutive coefficients of \(\tan^2x\). For \(r\) perturbed coefficients, a general power-series monotonicity theorem gives at most \(r\) interior critical points.
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