Abstract
We have proved that if the partial numerators of the continued fraction f(c)=1/1+c2/l+c3/l+... are all nonzero and for at least some number n⩾1 satisfy the inequalities
then f(c) converges in the wide sense if and only if at least one of the series
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Translated from Matematicheskie Zametki, Vol. 20, No. 5, pp. 665–674, November, 1976.
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Khloponin, S.S. Tests for the convergence of continued fractions, based on the fundamental system of inequalities. Mathematical Notes of the Academy of Sciences of the USSR 20, 933–938 (1976). https://doi.org/10.1007/BF01146913
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DOI: https://doi.org/10.1007/BF01146913