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Does anyone have a recommendation for a rigorous while readable book to use for the self study of continued fractions?


PS - As examples of "rigorous while readable book" for self-learning, A. Pressley's book on Differential Geometry and P. Fitzpatrick's book on Advanced Calculus are much better than the other books of same subjects.

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  • $\begingroup$ I don't know if Continued Fractions with Applications LORENTZEN, L.; WAADELAND, H. is good at all? $\endgroup$ – user231343 Apr 12 '16 at 16:16
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I would start with Khinchin's Continued Fractions . For $8.95 you can't go wrong, and you can move on to something more advanced when you're done.

http://store.doverpublications.com/0486696308.html

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  • $\begingroup$ I second this, Khinchin is a great introduction. $\endgroup$ – Lionel Ricci Apr 12 '16 at 16:00
  • $\begingroup$ In Ch.3, is "the measure theory" the same as the measure theory studied in advanced analysis? If so, then it must be so hard... $\endgroup$ – user231343 Apr 12 '16 at 16:04
  • $\begingroup$ @Edi Yes, that's the measure theory from advanced analysis, and you need the definitions after the first few pages. But Chapters 1 and 2 are elementary (no advanced course work required). You can see the style at google books. $\endgroup$ – Ethan Bolker Apr 12 '16 at 16:21
  • $\begingroup$ @Edi: The third chapter requires more background, but the first two are elementary. The presentation is clear but rather concise, and there’s little if anything that you can afford to skip. It’s definitely a book to be read with pen and paper handy. There are undoubtedly gentler introductions out there, but this is a very good one, well worth the price. $\endgroup$ – Brian M. Scott Apr 12 '16 at 22:04
  • $\begingroup$ @BrianM.Scott - Looking at contents and first pages, it looks that Neverending Fractions by Poorten .. should be the best choice for me, but I can't find a free or cheap ebook of it. Could you please send me if you a pdf of it? Thanks $\endgroup$ – user231343 Apr 13 '16 at 8:16

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