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Elliptic Functions by W. F. Eberlein, J. V. Armitage

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Appendix

A.1 Introduction

In this appendix we present an unorthodox (in some respects) sequence of simple propositions that update and make rigorous Euler’s elementary derivation of the product formulae for the sine and cosine and some related identities, to which we have appealed in the main text and which are also related to the approach to elliptic functions given by Eisenstein and Kronecker, see Weil [1975], where, indeed, another proof affording insight into the elliptic functions is given. We also include, for convenience of reference and to save overburdening other parts of the book, some propositions concerning the Benoulli numbers and related topics.

A.2 The formula for arg (z)

We begin by recalling the properties of the argument (amplitude) ...

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