Difference between revisions of "Manuals/calci/BASETHETA"

Revision as of 18:11, 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 $\tau$ .
So for each $\tau \in \mathbb {C}$ with $Im\tau >0$ 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 $\tau >0$ .
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.

@@ Line 5: / Line 5: @@
 *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 <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 .
+*The function <math>\theta</math> depends on <math>\tau</math> .
-*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.
+*So for each <math>\tau \in \mathbb{C}</math> with <math>Im \tau >  0</math> we get a (not necessarily different) basic theta function.
-*Hence there is a whole family of basic theta functions {\theta(\tau )}<math>\tau \in \mathbb{C}</math>τ∈C,Im <math>\tau\ge  0</math>.
+*Hence there is a whole family of basic theta functions <math>{\theta(\tau )},\tau \in \mathbb{C}</math>τ∈C,Im <math>\tau >  0</math>.
 *But here we assume <math>\tau</math> 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.