Changes

*This function shows the Base theta value.

*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 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.

*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.  

*The basic theta function is quasi-periodic.  

*Base Theta is locally uniformly unordered convergent also  basic theta function is an entire function.

*Base Theta is locally uniformly unordered convergent also  basic theta function is an entire function.