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  The Decipherment and Translation of Jacobi's Fundamenta Nova Theoriae Functionum Ellipticarum and Theorie der Elliptischen Functionen, aus den Eigenschaften der Thetareihen Abgeleitet.    I have deciphered and translated Jacobi's lectures on Thetareihen and substantial parts of his Fundamenta Nova into English. The work on the latter is in progress. (These two publications will be briefly referred to as the Thetareihen and the Fundamenta respectively.)   The work of decipherment and translation is three-fold: 1) The decipherment and translation of the Latin and the German prose into English. 2) The decipherment of the symbolic content and its translation into modern notation. 3) The decipherment of  the theoretical content of the Fundamenta  and its "translation", i.e its re-development, in terms of theta functions, in accordance with the contents of the  Thetareihen.   Of these, 3) is in its initial stages. 2) is complete. 1) is complete f...
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THE ELLIPTIC LOGARITHM FUNCTION

    In an earlier post I have discussed the elliptic exponential function                                    E(iu, k) = cn(u, k) +i sn(u, k)      By replacing u by -iu in this function we obtain the function E(u, k). When q approaches 0,  E(iu, k)  reduces to the exponential function e^iu = cos u + i sin u and E(u, k) reduces to e^u.  As is well-known, the inverse of the exponential function v = e^u is the logarithm function ln v =u, such that ln(1+v) = Σ (-1)^{n-1}. v^n /n                                                                                                       (1...
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