On Some Modular Equations and Their Applications I
Bull. Korean Math. Soc. 2013 Vol. 50, No. 3, 761-776
https://doi.org/10.4134/BKMS.2013.50.3.761
Printed May 31, 2013
Jinhee Yi, Man Gi Cho, Jeong Hwan Kim, Seong Hoi Lee, Jae Myung Yu, and Dae Hyun Paek
Korea Science Academy of KAIST, Korea Science Academy of KAIST, Korea Science Academy of KAIST, Korea Science Academy of KAIST, Korea Science Academy of KAIST, Busan National University of Education
Abstract : We derive several modular equations and present their proofs based on concise algebraic computations. In addition, we establish explicit relations and formulas for some parameterizations for the theta functions $\varphi$ and $\psi$ and show some applications of the modular equations to evaluations of the cubic continued fraction and the theta function $\psi$.
Keywords : theta functions, modular equations
MSC numbers : Primary 11F27, 33C90; Secondary 11F20, 33C05, 33C75
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