Difference between revisions of "Manuals/calci/BASETHETA"

Revision as of 17:08, 21 December 2016

BASETHETA (Theta)

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.

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 ==Description==
 *This function shows the Base theta value.
-*The basic theta function is defined to be the function <math> \theta</math>:<math>\mathbb{C} \rarr \mathbb{C} </math> given by
+*The basic theta function is defined to be the function <math> \theta</math>:<math>\mathbb{C} \rarr \mathbb{C} </math> given by <math>\theta(z):= \theta(\tau)(z):=\sum_{n\in z} exp(\pi in^2 \tau)exp(2\pi inz)</math>
 *The function <math>\theta</math> depends on <math>\tau</math>τ .
 *So for each <math>\tau \in \mathbb{C}</math> with <math>Im \tau \ge  0</math> we get a (not necessarily different) basic theta function.