DLMF:

20 Theta Functions Properties 20.2 Definitions and Periodic Properties 20.2 Definitions and Periodic Properties 20.3 Graphics

Figure 20.2.1 (See in context.)

Figure 20.2.1:

-plane. Fundamental parallelogram. Left-hand diagram is the rectangular case ( $\tau$ purely imaginary); right-hand diagram is the general case. $\bullet$ zeros of $\mathop{\theta_{{1}}\/}\nolimits\!\left(z\middle|\tau\right)$ , $\blacksquare$ zeros of $\mathop{\theta_{{2}}\/}\nolimits\!\left(z\middle|\tau\right)$ , $\blacktriangle$ zeros of $\mathop{\theta_{{3}}\/}\nolimits\!\left(z\middle|\tau\right)$ , $\blacklozenge$ zeros of $\mathop{\theta_{{4}}\/}\nolimits\!\left(z\middle|\tau\right)$ .

Annotations:

Symbols:: $\mathop{\theta_{{j}}\/}\nolimits\!\left(z\middle|\tau\right)$ : theta function, : complex and $\tau$ : lattice parameter
Permalink:: http://dlmf.nist.gov/20.2.F1.mag
Encodings:: Magnified png, Magnified png, pdf, pdf

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