A summation formula for divergent continued fractions
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Paradoxical formulas which have been proposed by a number of authors for evaluating divergent continued fractions are discussed. The point of the paradoxes is that limit passages (which are to be rigorously defined) result in the convergence real sequences to complex values. These formulas are refined and substantiated on the basis of the theory of uniform distribution supplemented with certain statements of complex analysis.
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- 2.V. I. Smirnov and V. S. Kulyabko, Mikhail Sofronov, a Russian Mathematician of the Middle of the Eighteenth Century (Izd. Akad. Nauk SSSR, Moscow, 1954) [in Russian].Google Scholar