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This subtopic studies convergence and divergence of infinite processes, including summability questions, asymptotic behavior, and the basic criteria that govern series and transforms.
40A05 develops convergence and divergence of series and sequences in convergence and divergence of infinite processes. Core themes include criteria for convergence behavior, structural inequalities, and summability principles used to characterize limiting behavior of sequences and series.
Wikipedia search: Convergence and divergence of series and sequences
Used to prove convergence or divergence under weakened hypotheses, compare summation methods, and transfer results between sequence spaces and functional-analytic formulations.
40A10 develops convergence and divergence of integrals in convergence and divergence of infinite processes. Core themes include criteria for convergence behavior, structural inequalities, and summability principles used to characterize limiting behavior of sequences and series.
Wikipedia search: Convergence and divergence of integrals
Used to prove convergence or divergence under weakened hypotheses, compare summation methods, and transfer results between sequence spaces and functional-analytic formulations.
40A15 develops convergence and divergence of continued fractions in convergence and divergence of infinite processes. Core themes include criteria for convergence behavior, structural inequalities, and summability principles used to characterize limiting behavior of sequences and series.
Wikipedia search: Convergence and divergence of continued fractions
Used to prove convergence or divergence under weakened hypotheses, compare summation methods, and transfer results between sequence spaces and functional-analytic formulations.
40A20 develops convergence and divergence of infinite products in convergence and divergence of infinite processes. Core themes include criteria for convergence behavior, structural inequalities, and summability principles used to characterize limiting behavior of sequences and series.
Wikipedia search: Convergence and divergence of infinite products
Used to prove convergence or divergence under weakened hypotheses, compare summation methods, and transfer results between sequence spaces and functional-analytic formulations.
40A25 develops approximation to limiting values in convergence and divergence of infinite processes. Core themes include criteria for convergence behavior, structural inequalities, and summability principles used to characterize limiting behavior of sequences and series.
Wikipedia search: Approximation to limiting values
Used to prove convergence or divergence under weakened hypotheses, compare summation methods, and transfer results between sequence spaces and functional-analytic formulations.
40A30 develops convergence and divergence of series and sequences of functions in convergence and divergence of infinite processes. Core themes include criteria for convergence behavior, structural inequalities, and summability principles used to characterize limiting behavior of sequences and series.
Wikipedia search: Convergence and divergence of series and sequences of functions
Used to prove convergence or divergence under weakened hypotheses, compare summation methods, and transfer results between sequence spaces and functional-analytic formulations.
40A35 develops ideal and statistical convergence in convergence and divergence of infinite processes. Core themes include criteria for convergence behavior, structural inequalities, and summability principles used to characterize limiting behavior of sequences and series.
Wikipedia search: Ideal and statistical convergence
Used to prove convergence or divergence under weakened hypotheses, compare summation methods, and transfer results between sequence spaces and functional-analytic formulations.