On the formation of continued fractions

Details On the formation of continued fractions On the formation of continued fractions

2005-08-12

arxiv.org/abs/math/0508227v1

Mathematics

History and Overview

17 pages, seems to be first English translation of Euler's Latin original ``De formatione fractionum continuarum'', Acta Acade

Scientific paper

In this paper Euler shows how, if we have recursive functions f,g,h and an
infinite sequence A,B,C,... which satisfies fA=gB+hC, f'B=g'C+h'D,
f''C=g''D+h''E, f'''D=g'''E+h'''F, etc., where the primes denote an index not a
derivative, then we can find a continued fraction for fA/B.

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