Ramanujan continued fractions via orthogonal polynomials

Solved via Continued Fractions

The purpose of this article is to provide criteria for the solvability of the Diophantine equation a2X2− bY 2 = c in terms of the simple continued fraction expansion of √ a2b, and to explore criteria for the solvability of AX2 − BY 2 = C for given A, B, C ∈ N in the general case. This continues work in [9]–[11].

Modular relations and explicit values of Ramanujan-Selberg continued fractions

By employing a method of parameterizations for Ramanujan's theta-functions, we find several modular relations and explicit values of the Ramanujan-Selberg continued fractions .

Orthogonal Rational Functions and Continued Fractions

On the 1D and 2D Rogers-Ramanujan Continued Fractions

In this paper the classical and generalized numerical Rogers Ramanujan continued fractions are extended to a polynomial continued fraction in one and two dimensions. Using the new continued fractions, the fundamental recurrence formulas and a fast algorithm, based on matrix formulations, are given for the computation of their transfer functions. The presented matrix formulations can provide a n...

Ramanujan and Extensions and Contractions of Continued Fractions

If a continued fraction K∞ n=1an/bn is known to converge but its limit is not easy to determine, it may be easier to use an extension of K∞ n=1an/bn to find the limit. By an extension of K ∞ n=1an/bn we mean a continued fraction K∞ n=1cn/dn whose odd or even part is K ∞ n=1an/bn. One can then possibly find the limit in one of three ways: (i) Prove the extension converges and find its limit; (ii...