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.
%0 Generic
%1 citeulike:3036274
%A Euler, Leonhard
%D 2005
%K Vor1800 available-in-tex-format mathematics number-theory pre1800
%T On the formation of continued fractions
%U http://arxiv.org/abs/math/0508227
%X 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.
@misc{citeulike:3036274,
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.},
added-at = {2009-08-02T17:14:35.000+0200},
archiveprefix = {arXiv},
author = {Euler, Leonhard},
biburl = {https://www.bibsonomy.org/bibtex/29f7344debb8ab65678299d0f5adb544e/rwst},
citeulike-article-id = {3036274},
citeulike-linkout-0 = {http://arxiv.org/abs/math/0508227},
citeulike-linkout-1 = {http://arxiv.org/pdf/math/0508227},
description = {my bookmarks from citeulike},
eprint = {math/0508227},
interhash = {be5f9d5f1c7e8c9ab9380c0cb9d4fc98},
intrahash = {9f7344debb8ab65678299d0f5adb544e},
keywords = {Vor1800 available-in-tex-format mathematics number-theory pre1800},
month = Aug,
posted-at = {2008-07-23 08:44:58},
priority = {2},
timestamp = {2009-08-06T10:20:24.000+0200},
title = {On the formation of continued fractions},
url = {http://arxiv.org/abs/math/0508227},
year = 2005
}