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The document defines and discusses Jacobian theta functions. It introduces the four Jacobian theta functions θ1, θ2, θ3, θ4 and describes their periodicity. It then expresses the three basic Jacobian elliptic functions as quotients of Jacobian theta functions. The document goes on to construct the simplest Jacobian theta function θ(w) by determining its Fourier series coefficients recursively. It shows the theta function θ(w) converges and has one zero per fundamental parallelogram. Finally, it defines thre

Author

胡政

Language

EN