On some modular equations and their applications II
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We first derive some modular equations of degrees 3 and 9 and present their concise proofs based on algebraic computations. We then use these modular equations to establish explicit relations and for- mulas for the parameterizations for the theta functions φ and ψ In ad- dition, we find specific values of the parameterizations to evaluate some numerical values of the cubic continued fraction.
Abstract
We first derive some modular equations of degrees 3 and 9 and present their concise proofs based on algebraic computations. We then use these modular equations to establish explicit relations and for- mulas for the parameterizations for the theta functions φ and ψ In ad- dition, we find specific values of the parameterizations to evaluate some numerical values of the cubic continued fraction.
참고문헌 (10)
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- R. A. Rankin, "Modular Forms and Functions" (1977), Cambridge University Press
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- J. Yi, "The Construction and Applications of Modular Equations", 박사, pp.2001
- J. Yi, "Theta-function identities and the explicit formulas for theta-function and their applications", J. Math. Anal. Appl, 292(2), pp.381~400 (2004)
- 백대현, "On Some Modular Equations and Their Applications I", 대한수학회보, 50(3), pp.761~776 (2013), 대한수학회
- J. Yi, "The explicit formulas and evaluations of Ramanujan’s theta-function", J. Math. Anal. Appl, 321(1), pp.157~181 (2006)