Results 61 to 70 of about 1,452,959 (130)
Arithmetic of the Ramanujan–Göllnitz–Gordon continued fraction [PDF]
, 2009 TextWe extend the results of Chan and Huang [H.H. Chan, S.-S. Huang, On the Ramanujan–Göllnitz–Gordon continued fraction, Ramanujan J. 1 (1997) 75–90] and Vasuki, Srivatsa Kumar [K.R. Vasuki, B.R. Srivatsa Kumar, Certain identities for Ramanujan–Göllnitz–
Cho, Bumkyu +2 more
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On the infinite Borwein product raised to a positive real power. [PDF]
Ramanujan J, 2023 Schlosser MJ, Zhou NH.
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Certain identities for Ramanujan–Göllnitz–Gordon continued fraction [PDF]
, 2006 In this paper, we present three new identities providing relations between Ramanujan–Göllnitz–Gordon continued fraction H(q) and the three continued fractions H(q5), H(q7) and H(q11). We also give a new approach for relations between H(q) and H(q3) which
Srivatsa Kumar, B.R., Vasuki, K.R.
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Rogers-Ramanujan continued fraction and approximations to $\mathbf{2π}$
, 2023 We observe that certain famous evaluations of the Rogers-Ramanujan continued fraction $R(q)$ are close to $2π-6$ and $(2π-6)/2π$, and that $2π-6$ can be expressed by a Rogers-Ramanujan continued fraction in which $q$ is very nearly equal to $R^5(e^{-2π})$. The value of $-{5\over α}\ln R(e^{-2απ})$ converges to $2π$ as $α$ increases.
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Hadamard products for generalized Rogers–Ramanujan series [PDF]
, 2008 The purpose of this paper is to derive product representations for generalizations of the Rogers–Ramanujan series. Special cases of the results presented here were first stated by Ramanujan in the “Lost Notebook” and proved by George Andrews.
Huber, Timothy, Huber, Tim
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On the Divergence of the Rogers-Ramanujan Continued Fraction on the Unit Circle [PDF]
, 2004 This paper is an intensive study of the convergence of the Rogers-Ramanujan continued fraction. Let the continued fraction expansion of any irrational number t ∈ (0, 1) be denoted by [0, a1(t), a2(t), · · · ] and let the i-th convergent of this continued
Bowman, Douglas, McLaughlin, James
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Some continued fractions of the Rogers-Ramanujan type
Duke Mathematical Journal, 1965 The author proves that the continued fraction \((\vert x\vertn_2 \ge n_3 > n_4 \ge \ldots\) are equinumerous with those whose parts are either odd or \(\equiv\pm 4\pmod{20}\). This complements Euler's theorem that the partitions of any natural number into distinct parts are equinumerous with those into odd parts.
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Rational Approximation to a New Generalization of the Rogers–Ramanujan Continued Fraction
Journal of Number Theory, 2000 The authors give an irrationality measure for the values at some rational points of the continued fraction \[ G(x,y,z)=1+{xyz\over 1+} {xy^2 z^{2^2} \over 1+}{xy^3z^{3^2} \over 1+\cdots} {xy^nz^{n^2}\over 1+\cdots} \] and prove this irrationality measure to be best possible. The method is basically the same as in [\textit{I. Shiokawa}, Acta Arith.
Bowman, Douglas, Choi, Geumlan
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Singular values of the Rogers-Ramanujan continued fraction
, 1999 Let $z\in\C$ be imaginary quadratic in the upper half plane.Then the Rogers-Ramanujan continued fraction evaluated at $q=e^{2\pi i z}$ is contained in a class field of $\Q(z)$.
Honsbeek, M, Gee, A.C.P.
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Some Theorems on Ramanujan's Cubic Continued Fraction and Related Identities [PDF]
, 2008 On page 366 of his lost notebook [8], Ramanujan has recorded cubic continued fraction and several theorems analogous to Rogers-Ramanujan continued fractions.
Naika, M.S.M.
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