Finite Rogers-Ramanujan type continued fractions
نویسندگان
چکیده
منابع مشابه
Finite Rogers-Ramanujan Type Identities
Polynomial generalizations of all 130 of the identities in Slater’s list of identities of the Rogers-Ramanujan type are presented. Furthermore, duality relationships among many of the identities are derived. Some of the these polynomial identities were previously known but many are new. The author has implemented much of the finitization process in a Maple package which is available for free do...
متن کاملOn 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...
متن کاملOn the Generalized Rogers–ramanujan Continued Fraction
On page 26 in his lost notebook, Ramanujan states an asymptotic formula for the generalized Rogers–Ramanujan continued fraction. This formula is proved and made slightly more precise. A second primary goal is to prove another continued fraction representation for the Rogers–Ramanujan continued fraction conjectured by R. Blecksmith and J. Brillhart. Two further entries in the lost notebook are e...
متن کاملNew Finite Rogers-Ramanujan Identities
We present two general finite extensions for each of the two Rogers-Ramanujan identities. Of these one can be derived directly from Watson’s transformation formula by specialization or through Bailey’s method, the second similar formula can be proved either by using the first formula and the q-Gosper algorithm, or through the so-called Bailey lattice.
متن کاملParametric Evaluations of the Rogers-Ramanujan Continued Fraction
In this paper with the help of the inverse function of the singular moduli we evaluate the Rogers-Ranmanujan continued fraction and its first derivative. 1 q 1 1 q 2 1 q 3 1 · · ·. 1.1 We also define a; q n : n−1 k0 1 − aq k , f −q : ∞ n1 1 − q n q; q ∞ .
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ژورنال
عنوان ژورنال: Journal of Algebra Combinatorics Discrete Structures and Applications
سال: 2018
ISSN: 2148-838X
DOI: 10.13069/jacodesmath.451218