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

Jump to navigation
Jump to search

(10 intermediate revisions by 2 users not shown) | |||

Line 4: | Line 4: | ||

==Description== | ==Description== | ||

*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 : \mathbb{C} | + | *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> | + | *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 { | + | *Hence there is a whole family of basic theta functions <math>{\theta(\tau )},\tau \in \mathbb{C}</math>,Im <math>\tau > 0</math>. |

− | *But here we assume | + | *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. | ||

+ | |||

+ | ==Examples== | ||

+ | #BASETHETA(45) = 1.0177028497428964 | ||

+ | #BASETHETA(90) = 2.0354056994857928 | ||

+ | #BASETHETA(8640) = 0.6202026280698192 | ||

+ | |||

+ | ==Related Videos== | ||

+ | |||

+ | {{#ev:youtube|v=hTGhCGrPLmw|280|center|Trigonometric Angles}} | ||

+ | |||

+ | ==See Also== | ||

+ | *[[Manuals/calci/DEGREES | DEGREES]] | ||

+ | *[[Manuals/calci/RADIANS | RADIANS]] | ||

+ | *[[Manuals/calci/ANGLE | ANGLE]] | ||

+ | |||

+ | ==References== | ||

+ | [http://www.maths.tcd.ie/pub/ims/bull60/R6004.pdf Theta Functions] | ||

+ | |||

+ | |||

+ | |||

+ | *[[Z_API_Functions | List of Main Z Functions]] | ||

+ | |||

+ | *[[ Z3 | Z3 home ]] |

## Latest revision as of 14:48, 10 December 2018

**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 ,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.

## Examples

- BASETHETA(45) = 1.0177028497428964
- BASETHETA(90) = 2.0354056994857928
- BASETHETA(8640) = 0.6202026280698192

## Related Videos

## See Also

## References