We extend the telescoping-sequence framework from functions and differential equations tointegral operators. Building on optimally telescoping exponential approximants, we constructoperator-level telescoping expansions for Laplace and Fourier transforms, Volterra convolutionoperators, and strongly continuous semigroups. We prove that if an integral kernel is expressibleas a finite algebraic combination of exponentials (or matrix exponentials), then the associatedoperator admits telescoping approximants whose successive differences decay as O(n−(k+1))whenever the underlying exponential engine has order k.Our results provide explicit, closed-form operator approximations with quantified tail bounds,and unify telescoping methods for constants, functions, ODEs, and integral transforms withina single analytical framework. Complete Python implementation is provided in Appendix B.Code will be available at https://github.com/jpbald93/telescoping-operators upon publication(January 2026).
Joshua Bald (Fri,) studied this question.