Śleszyński–Pringsheim theorem: Difference between revisions
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In mathematics, the '''Śleszyński–Pringsheim theorem''' is a statement about convergence of certain [[continued fraction]]s, discovered by [[Ivan Śleszyński]] and [[Alfred Pringsheim]] in the late 19th century. |
In mathematics, the '''Śleszyński–Pringsheim theorem''' is a statement about convergence of certain [[continued fraction]]s, discovered by [[Ivan Śleszyński]] and [[Alfred Pringsheim]] in the late 19th century. |
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Revision as of 15:45, 12 September 2011
In mathematics, the Śleszyński–Pringsheim theorem is a statement about convergence of certain continued fractions, discovered by Ivan Śleszyński and Alfred Pringsheim in the late 19th century.
It states that if an, bn, for n = 1, 2, 3, ... are real numbers and |bn| ≥ |an| + 1 for all n, then
converges absolutely to a number ƒ satisfying 0 < |ƒ| < 1.[1]
Notes and references
- ^ Lisa Lorentzen and Haakon Waadeland, Continued Fractions: Convergence theory, Atlantic Press, 2008, page 129