ARITHMETIC OF INFINITE PRODUCTS AND ROGERS-RAMANUJAN CONTINUED FRACTIONS
نویسندگان
چکیده
منابع مشابه
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...
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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...
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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 ∞ .
متن کاملThe Rogers-Ramanujan continued fraction and its level 13 analogue
One of the properties of the Rogers-Ramanujan continued fraction is its representation as an infinite product given by r(q) = q ∞ ∏
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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...
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ژورنال
عنوان ژورنال: Communications of the Korean Mathematical Society
سال: 2007
ISSN: 1225-1763
DOI: 10.4134/ckms.2007.22.3.331