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2. Solving quadratic equations with continued fractions

   en.wikipedia.org/wiki/Solving_quadratic...

   If this infinite continued fraction converges at all, it must converge to one of the roots of the monic polynomial x 2 + bx + c = 0. Unfortunately, this particular continued fraction does not converge to a finite number in every case. We can easily see that this is so by considering the quadratic formula and a monic polynomial with real ...

3. Continued fraction - Wikipedia

   en.wikipedia.org/wiki/Continued_fraction

   Another meaning for generalized continued fraction is a generalization to higher dimensions. For example, there is a close relationship between the simple continued fraction in canonical form for the irrational real number α, and the way lattice points in two dimensions lie to either side of the line y = αx. Generalizing this idea, one might ...

4. Simple continued fraction - Wikipedia

   en.wikipedia.org/wiki/Simple_continued_fraction

   A simple or regular continued fraction is a continued fraction with numerators all equal one, ... Step Real Number Integer part ... Math. Z. 78: 361–374. doi:10. ...

5. Category:Continued fractions - Wikipedia

   en.wikipedia.org/wiki/Category:Continued_fractions

   In mathematics, regular continued fractions play an important role in representing real numbers, and have a rich general theory touching on a variety of topics in number theory. Moreover, generalized continued fractions have important and interesting applications in complex analysis .

6. Rogers–Ramanujan continued fraction - Wikipedia

   en.wikipedia.org/wiki/Rogers–Ramanujan...

   The Rogers–Ramanujan continued fraction is a continued fraction discovered by Rogers (1894) and independently by Srinivasa Ramanujan, and closely related to the Rogers–Ramanujan identities. It can be evaluated explicitly for a broad class of values of its argument.

7. Euler's continued fraction formula - Wikipedia

   en.wikipedia.org/wiki/Euler's_continued_fraction...

   Euler derived the formula as connecting a finite sum of products with a finite continued fraction. (+ (+ (+))) = + + + + = + + + +The identity is easily established by induction on n, and is therefore applicable in the limit: if the expression on the left is extended to represent a convergent infinite series, the expression on the right can also be extended to represent a convergent infinite ...