%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 }