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Showing 1 to 12 of 12 for “"Ramanujan's Lost Notebook"”.
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Theorems on Theta Functions in Ramanujan's Lost Notebook
Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs
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Tenth Order Mock Theta Functions in Ramanujan's Lost Notebook
S. Ramanujan's last letter to G. H. Hardy contains the definition of mock theta functions, a list of 17 mock theta functions, and 5 identities related to mock theta functions. Also, Ramanujan's lost notebook contains many further results on mock theta functions. In particular, the lost notebook …
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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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Investigations Into Cranks of Partitions, Trigonometric Sums, and Q-Integrals
… of integrals found on page 201 of Ramanujan's Lost Notebook. We also prove several results related to the integrals on page 201. Our integral evaluations follow from well-known product-series identities from the theory of q-series.
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Q-Continued Fractions and Related Q-Series
… 5, we prove two other equations on page 45 of Ramanujan's lost notebook by using the Bauer-Muir transformation and by using the method of successive approximation. Also, we prove several continued fractions of Ramanujan which are related to the odd parts of continued fractions.
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Arithmetic of partition functions and q-combinatorics
… proofs for q-series identities appearing in Ramanujan's lost notebook and give combinatorial interpretations for third and sixth order mock theta functions.
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Identities involving theta functions and analogues of theta functions
… 1, we give a completely elementary proof of Ramanujan's circular summation formula of theta functions and its generalizations given by S. H. Chan and Z. -G. Liu, and J. M. Zhu, who used the theory of elliptic functions. In contrast to all other proofs, our proofs are elementary. An …
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Contributions to Trigonometric Sums and Fifth -Order Mock Theta Functions
… The second portion of this thesis focuses on Ramanujan's mock theta functions. In the second chapter, we extend the work of G. N. Watson on the fifth order mock theta functions, and show that in comparison to the third order functions, the fifth order mock theta functions possess a more …
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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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Product Identities for Theta Functions
… in [34], and identities involving septic Rogers-Ramanujan functions obtained by H. Hahn in [29], are shown to be special cases of this general formula. We also obtain a generalization of the septuple product identity. Several entries in Ramanujan's notebooks as well as new identities are proved …
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Transformation formulas associated with integrals involving the Riemann Ξ-function and rank-crank type PDEs in partition theory
… found on page 220 in the volume ``Ramanujan's lost notebook and other unpublished papers''. In Chapter 2, we give two different proofs of this result, the second one being implicitly sought by A.P.~Guinand while rediscovering this result. However, Guinand only partially rediscovered …
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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