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Theorem B. If the inequalities (1) hold for rp of even index, no «2j>=0, r2pi < 1, i= 1, 2, 3, • • • , X)(l~~ r*p>) diverges, and v is the point in the extended complex plane to which the odd part of fia) converges at least in the wider sense, then every neighborhood of v contains infinitely many even approximants of fia). A similar result holds if the roles of even and odd indices are interchanged.

A theorem on continued fractions and the fundamental inequalities