Śleszyński–Pringsheim theorem

In mathematics, the Śleszyński–Pringsheim theorem is a statement about convergence of certain continued fractions.

It was discovered by Ivan Śleszyński[1] and Alfred Pringsheim[2] in the late 19th century.

[3] It states that if

are real numbers and

, then converges absolutely to a number

,[4] meaning that the series where

are the convergents of the continued fraction, converges absolutely.

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