Abstract
This chapter discusses the concept of an elliptic function. The circular and hyperbolic functions are represented as polynomial functions of sin σ, cos σ, sinh σ, and cosh σ, whereas the lemniscate functions are represented as fractional expressions in terms of s1 σ, cl σ, s1 τ, and cl τ and the Jacobian functions are expressed as fractional expressions in terms of the Jacobian functions of the real variables σ and τ. Therefore, the functions sin t, cos t, sinh t, and cosh t are defined and have finite values for every complex.
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