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Showing 1 to 10 of 10 for “"Elliptic functions"”.
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Swan Modules and Elliptic Functions
… of certain Kummer extensions with respect to an elliptic group law. He has obtained elliptic analogues of cyclotomic results. The arithmetic nature of elliptic resolvents, the elliptic analogue of the Gauss sum conductor formula and the strength of the elliptic group law being a Lubin-Tate formal …
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Infinite Series Identities in the Theory of Elliptic Functions and Q-Series
… transformation by integrating some selected functions over a positively oriented polygon, generalizing Siegel's integration over a parallelogram. As consequences, we obtain a generalization of the Dedekind-eta function transformation and generalizations of other transformation formulas. In …
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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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Cubic theta functions and identities for Appell's F1 function
… three topics: the theory of the cubic theta functions 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 …
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Identities involving theta functions and analogues of theta functions
… mainly about various identities involving theta functions and analogues of theta functions. In Chapter 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 …
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Frequencies of Bound Geodesics, Angle of Deflection For Null Geodesics In Kerr Space-Time, and Gravitational Anomalies In Gravastars.
… can be written fully in terms of the canonical elliptic functions and the constants of the motion. We study some limiting examples, namely far away, or keplerian approximation, and the low eccentricity case. And we also extend our results to non-bound null geodesics, finding an exact result for …
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Some mixed and associated boundary value problems in the theory of thin plates
… the bending moments in terms of Weierstrassian elliptic functions. Another numerical example is included for a uniformly loaded plate clamped over a portion of one edge and simply- supported over the remainder of its boundary.
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On The Dynamics Of Systems With Vastly Different Frequencies
… oscillators 1 and 2 are found in terms of Jacobi elliptic functions. For coupling strengths exceeding critical bifurcation values, the limit cycle of oscillator 1 or 2 is found to disappear. In the second problem, we consider a simple pendulum coupled to a horizontal mass-spring system of a much …