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 </math>:<math> \mathbb{C} → \mathbb{C} </math> given by | + | *The basic theta function is defined to be the function <math> \theta</math>:<math>\mathbb{C} → \mathbb{C} </math> given by |
*The function <math>\theta</math> depends on <math>\tau</math>τ . | *The function <math>\theta</math> depends on <math>\tau</math>τ . | ||
*So for each <math>\tau \in \mathbb{C}</math>τ ∈ C with Im τ > 0 we get a (not necessarily different) basic theta function. | *So for each <math>\tau \in \mathbb{C}</math>τ ∈ C with Im τ > 0 we get a (not necessarily different) basic theta function. | ||
Revision as of 16:06, 21 December 2016
BASETHETA (Theta)
- is the angle value.
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 (syntax error): {\displaystyle \mathbb{C} → \mathbb{C} } given by
- The function depends on τ .
- So for each τ ∈ C with Im τ > 0 we get a (not necessarily different) basic theta function.
- Hence there is a whole family of basic theta functions {θ(τ )}τ∈C,Im τ>0.
- But here we assume τ 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.
:Failed to parse (syntax error): {\displaystyle \mathbb{C} → \mathbb{C} }
given by
τ .
τ ∈ C with Im τ > 0 we get a (not necessarily different) basic theta function.