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20 Theta FunctionsProperties20.3 Graphics
Figure 20.3.2 (See in context.)
See accompanying text
Figure 20.3.2: θ1⁡(π⁢x,q), 0≤x≤2, q = 0.05, 0.5, 0.7, 0.9. For q≤qDedekind, θ1⁡(π⁢x,q) is convex in x for 0<x<1. Here qDedekind=e−π⁢y0=0.19 approximately, where y=y0 corresponds to the maximum value of Dedekind’s eta function η⁡(i⁢y) as depicted in Figure 23.16.1.
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