Manuals/calci/BASETHETA

BASETHETA (Theta)

• $Theta$ is the angle value.

Description

• This function shows the Base theta value.
• The basic theta function is defined to be the function $\theta$:$\mathbb {C} \rightarrow \mathbb {C}$ given by $\theta (z):=\theta (\tau )(z):=\sum _{n\in z}exp(\pi in^{2}\tau )exp(2\pi inz)$
• The function $\theta$ depends on $\tau$τ .
• So for each $\tau \in \mathbb {C}$ with $Im\tau \geq 0$ we get a (not necessarily different) basic theta function.
• Hence there is a whole family of basic theta functions {\theta(\tau )}$\tau \in \mathbb {C}$τ∈C,Im $\tau \geq 0$.
• But here we assume $\tau$ to be fixed, so we have only one basic theta function.
• The basic theta function is quasi-periodic.
• Base Theta is locally uniformly unordered convergent also basic theta function is an entire function.