Relation To The Weierstrass Elliptic Function
The theta function was used by Jacobi to construct (in a form adapted to easy calculation) his elliptic functions as the quotients of the above four theta functions, and could have been used by him to construct Weierstrass's elliptic functions also, since
where the second derivative is with respect to z and the constant c is defined so that the Laurent expansion of at z = 0 has zero constant term.
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