Śleszyński–Pringsheim_theorem
Śleszyński–Pringsheim theorem
Criterion for convergence of continued fractions
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 , , for are real numbers and for all , then
converges absolutely to a number satisfying ,[4] meaning that the series
where are the convergents of the continued fraction, converges absolutely.