ON SOME MODULAR EQUATIONS OF DEGREE 5 AND THEIR APPLICATIONS

Title & Authors
ON SOME MODULAR EQUATIONS OF DEGREE 5 AND THEIR APPLICATIONS
Paek, Dae Hyun; Yi, Jinhee;

Abstract
We first derive several modular equations of degree 5 and present their concise proofs based on algebraic computations. We then establish explicit relations and formulas for some parameterizations for the theta functions $\small{{\varphi}}$ and $\small{{\psi}}$ by using the derived modular equations. In addition, we find specific values of the parameterizations and evaluate some numerical values of the Rogers-Ramanujan continued fraction.
Keywords
theta functions;modular equations;continued fractions;
Language
English
Cited by
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