Complex Variable Analysis
As remarked in section 2.2, the general definition of an elliptic function is that it is a doubly periodic function, all of whose singularities (except at infinity) are poles. In section 2.3, we commented on the existence of primitive periods characterized by the property that any period is expressible as the sum of multiples of these primitive periods; we also distinguished between primitive periods and fundamental periods, a fundamental period being defined to be such that no submultiple is a period. We shall commence this chapter by proving the existence of primitive periods.
KeywordsElliptic Function Multivalued Function Fourier Expansion Fundamental Period Jacobian Function
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