This approach demonstrates improved convergence in analytic functions, suggesting enhanced sequence design for targeting specific values.
We extend the telescoping sequence design framework developed for exponential constantsec to general analytic functions f(x). Given a target function f on an intervaland a desired telescoping order k ≥ 1, we construct explicit sequences {xn(x)} such thatxn(x) → f(x) with Dn(x) = xn+1(x) − xn(x) = O(n−(k+1)) uniformly for x in compactsubsets of the domain.
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Joshua Bald (2026) studied this question.
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