## Elliptic Functions According to Eisenstein and Kronecker"As a contribution to the history of mathematics, this is a model of its kind. While adhering to the basic outlook of Eisenstein and Kronecker, it provides new insight into their work in the light of subsequent developments, right up to the present day. As one would expect from this author, it also contains some pertinent comments looking into the future. It is not however just a chapter in the history of our subject, but a wide-ranging survey of one of the most active branches of mathematics at the present time. The book has its own very individual flavour, reflecting a sort of combined Eisenstein-Kronecker-Weil personality. Based essentially on Eisenstein's approach to elliptic functions via infinite series over lattices in the complex plane, it stretches back to the very beginnings on the one hand and reaches forward to some of the most recent research work on the other. (...) The persistent reader will be richly rewarded." |

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### Contents

Introduction | 3 |

Trigonometric Functions | 6 |

The Basic Elliptic Functions | 14 |

Basic Relations and Infinite Products | 22 |

Variation I | 35 |

Variation II | 42 |

Prelude to Kronecker | 51 |

Kroneckers Double Series | 69 |

Finale Allegro con brio | 87 |