DLMF: Figure 21.4.1 ‣ §21.4 Graphics ‣ Properties ‣ Chapter 21 Multidimensional Theta Functions

Figure 21.4.1 (See in context.)

Figure 21.4.1:

\hat{\theta}\left(\mathbf{z}\middle|\boldsymbol{{\Omega}}\right)

parametrized by (21.4.1). The surface plots are of

\hat{\theta}\left(x+iy,0\middle|\boldsymbol{{\Omega}}\right)

0\leq x\leq 1

0\leq y\leq 5

(suffix 1);

\hat{\theta}\left(x,y\middle|\boldsymbol{{\Omega}}\right)

0\leq x\leq 1

0\leq y\leq 1

(suffix 2);

\hat{\theta}\left(ix,iy\middle|\boldsymbol{{\Omega}}\right)

0\leq x\leq 5

0\leq y\leq 5

(suffix 3). Shown are the real part (a), the imaginary part (b), and the modulus (c).

ⓘ

Symbols:: $\hat{\theta}\left(\NVar{\mathbf{z}}\middle|\NVar{\boldsymbol{{\Omega}}}\right)$ : scaled Riemann theta function, $\mathrm{i}$ : imaginary unit and $\boldsymbol{{\Omega}}$ : a Riemann matrix
Permalink:: http://dlmf.nist.gov/21.4.F1h.viz

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