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Showing 1 to 6 of 6 for “"Rogers-Ramanujan continued fraction"”.
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The Rogers -Ramanujan Continued Fraction and a Certain Quotient of ETA Functions Found in Ramanujan's Lost Notebook
… which is essential for an elementary proof for Ramanujan's famous partition identity modulo 11, p(11n + 6) ≡ 0 (mod 11) is provided in the last part of the thesis.
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Generalizations of Certain Results on Continued Fraction
In this thesis we study generalizations of the Rogers-Ramanujan continued fraction. The Rogers-Ramanujan continued fraction arises from a three-term q-difference equation. We consider (m + 1)-term q-difference equations and also a generalization of the continued fraction algorithm called a …
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On the Convergence and Divergence of Q-Continued Fractions on and Off the Unit Circle
… implies general convergence. We show that all continued fractions in a certain class, which includes the Rogers-Ramanujan continued fractions and the three ""Ramanujan-Selberg"" continued fractions, diverge in the general sense at an uncountable set of points on the unit circle. We also show …
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Modular equations and Ramanujan's cubic and quartic theories of theta functions
… thesis, we prove several identities involving Ramanujan's general theta function. In Chapter 2, we give proofs for new Ramanujan type modular equations discovered by Somos and establish applications of some of them. In Chapter 3, we will give proofs for several Dedekind eta product identities …
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Contributions to the Theory of Q-Series and Mock Theta Functions
… time, a series of four related identities from Ramanujan's lost notebook. These are one-parameter identities which would directly imply some of the relations for the third order mock theta functions given by Ramanujan. In Chapter 3, we prove very general theorems on the periodicity of signs of …
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Modular identities for the Rogers-Ramanujan functions and analogues
Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by William Ingram (wingram2@illinois.edu) on 2011-01-21T22:47:37Z Item is restricted until 2013-01-21T22:47:37Z