The Seidel, Stern, Stolz and Van Vleck Theorems on continued fractions
نویسندگان
چکیده
The usual proofs of these three classical theorems are based on the sequences bn, An and Bn, where Zn = An/Bn, and the three-term recurrence relations for An and Bn. Our aim is to unify and generalise these results by giving new, geometric, proofs (apart from the elementary monotonicity statement, and subsequent convergence, in Theorem 1.1). First, however, we restate these three results (again, apart from the monotonicity) in a more concise way in the two following theorems.
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The Open University ’ s repository of research publications and other research outputs The Seidel , Stern , Stolz and Van Vleck Theorems on continued fractions
We unify and extend three classical theorems in continued fraction theory, namely the SternStolz Theorem, the Seidel-Stern Theorem and Van Vleck’s Theorem. Our arguments use the group of Möbius transformations both as a topological group and as the group of conformal isometries of three-dimensional hyperbolic space.
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