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There are a number of notational systems for the Jacobi theta functions. The notations given in the Wikipedia article define the original function
which is equivalent to
where q = e π i τ {\displaystyle q=e^{\pi i\tau }} and w = e π i z {\displaystyle w=e^{\pi iz}}.
However, a similar notation is defined somewhat differently in Whittaker and Watson, p. 487:
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