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Showing 1 to 8 of 8 for “"modular equations"”.
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The Construction and Applications of Modular Equations
We introduce also two parametrizations hk,n and h'k,n of the theta-function 4q . For q=e2piz , Im z > 0, define 4q : =fq,q=n =-infinityinfinityqn2 =:q30,2z , where q3 is classical theta function. For any positive real numbers n and k, define hk,n=4e-p n/k k1/44e-p nk=q 30,-n/k k1/4q30, -nk and …
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Modular equations and Ramanujan's cubic and quartic theories of theta functions
… 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 which Somos discovered through computational searches and which Choi discovered in his …
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Contributions to Ramanujan's continued fractions, class invariants, partition identities and modular equations
Various topics related to the work of Ramanujan are discussed in this thesis. In Chapter 2, we give a new proof of Ramanujan's famous partition identity modulo 5 (see (1.1)). This proof is an improvement of W. N. Bailey's proof given in 1952. We also establish a new proof of Ramanujan's partition …
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Contributions to Ramanujan's Theories of Modular Equations, Ramanujan-Type Series for 1/pi, and Partitions
Embargo set by: Seth Robbins for item 88266 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs
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Cubic theta functions and identities for Appell's F1 function
… as functions of two analytic variables, cubic modular equations, and a class of two-variable cubic modular equations. Chapter 2 is dedicated to the rst two topics, while Chapter 3 covers the last. First, the theory of cubic theta functions can be developed analogously to, but distinct from, the …
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Zeros of Generalized Rogers -Ramanujan Series and Topics From Ramanujan's Theory of Elliptic Functions
Chapter 5 is devoted to the derivation of modular equations analogous to relations given by Ramanujan in Chapter 21 of his Second Notebook. We also use trigonometric interpolation to write many of Ramanujan's identities in terms of the Weierstrass ℘-function.
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Eisenstein Series, Analogues of the Rogers -Ramanujan Functions, and Partition Identities
… Fine and R. J. Evans to construct analogues of modular equations, and then derive new identities satisfied by n=0infinity p(ln + k) qn, where p(n) is the ordinary partition function, l is an odd prime, and 0 ≤ k ≤ (l - 1).
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Infinite Series Identities in the Theory of Elliptic Functions and Q-Series
… Using these identities, we can derive certain modular equations. In Chapter 6, we evaluate certain infinite series involving hyperbolic functions by using the cubic theory of elliptic functions.