Difference between revisions of "Manuals/calci/BASETHETA"
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==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)
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Theta } is the angle value.
Description
- This function shows the Base theta value.
- The basic theta function is defined to be the function Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta} :Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbb{C} \rarr \mathbb{C} } given by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta(z):= \theta(\tau)(z):=\sum_{n\in z} exp(\pi in^2 \tau)exp(2\pi inz)}
- The function Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta} depends on Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau} .
- So for each Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau \in \mathbb{C}} with Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Im \tau > 0} we get a (not necessarily different) basic theta function.
- Hence there is a whole family of basic theta functions Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\theta(\tau )},\tau \in \mathbb{C}} ,Im Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau > 0} .
- But here we assume Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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.
Examples
- BASETHETA(45) = 1.0177028497428964
- BASETHETA(90) = 2.0354056994857928
- BASETHETA(8640) = 0.6202026280698192
Related Videos
See Also
References