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  2. 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.

  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. Solving quadratic equations with continued fractions - Wikipedia

    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 ...

  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. Continued fraction expansion - Wikipedia

    en.wikipedia.org/wiki/Continued_fraction_expansion

    Download as PDF; Printable version; In other projects ... For the continued fraction expansion. of a number, see simple continued fraction, of a function, see ...

  7. Simple continued fraction - Wikipedia

    en.wikipedia.org/wiki/Simple_continued_fraction

    Every finite continued fraction represents a rational number, and every rational number can be represented in precisely two different ways as a finite continued fraction, with the conditions that the first coefficient is an integer and the other coefficients are positive integers. These two representations agree except in their final terms.

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