The Seidel, Stern, Stolz and Van Vleck Theorems on continued fractions

نویسندگان

  • Alan F. Beardon
  • Ian Short
  • ALAN F. BEARDON
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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تاریخ انتشار 2010