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On the formation of continued fractions

Leonhard Euler
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Abstract

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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Leonhard Euler. 2005-08-12. On the formation of continued fractions. https://arxiv.org/abs/math/0508227

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