# Difference between revisions of "Manuals/calci/BASETHETA"

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*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> | + | *The function <math>\theta</math> depends on <math>\tau</math> . |

− | *So for each <math>\tau \in \mathbb{C}</math> with <math>Im \tau | + | *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 )} | + | *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. |

## Revision as of 18:11, 21 December 2016

**BASETHETA (Theta)**

- is the angle value.

## Description

- This function shows the Base theta value.
- The basic theta function is defined to be the function : given by
- The function depends on .
- So for each with we get a (not necessarily different) basic theta function.
- Hence there is a whole family of basic theta functions τ∈C,Im .
- But here we assume 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.