Difference between revisions of "Manuals/calci/BASETHETA"

Latest revision as of 14:48, 10 December 2018

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 ${\theta (\tau )},\tau \in \mathbb {C}$ ,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.

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+<div style="font-size:30px">'''BASETHETA (Theta)'''</div><br/>
+*<math> Theta </math> is the angle value.
+==Description==
+*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> .
+*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 <math>{\theta(\tau )},\tau \in \mathbb{C}</math>,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.
+==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 ]]