DLMF:27.13.E6 (Q8098): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: alternative notation / rank
 
Normal rank
Property / Symbols used: alternative notation / qualifier
 
Defining formula:

ϑ ⁡ ( x ) = θ 3 ⁡ ( 0 , x ) a-theta-function 𝑥 Jacobi-theta 3 0 𝑥 {\displaystyle{\displaystyle\vartheta\left(\NVar{x}\right)=\theta_{3}\left(0,x% \right)}}

\AThetaFunction@{\NVar{x}}=\Jacobithetaq{3}@{0}{x}
Property / Symbols used: alternative notation / qualifier
 
xml-id: C27.S13.E4.m2abdec

Revision as of 14:29, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:27.13.E6
No description defined

    Statements

    Defining formula
    ( ϑ ⁡ ( x ) ) 2 = 1 + 4 ⁢ ∑ n = 1 ∞ ( δ 1 ⁢ ( n ) - δ 3 ⁢ ( n ) ) ⁢ x n , superscript a-theta-function 𝑥 2 1 4 superscript subscript 𝑛 1 subscript 𝛿 1 𝑛 subscript 𝛿 3 𝑛 superscript 𝑥 𝑛 {\displaystyle{\displaystyle(\vartheta\left(x\right))^{2}=1+4\sum_{n=1}^{% \infty}\left(\delta_{1}(n)-\delta_{3}(n)\right)x^{n},}}
    0 references
    DLMF id
    DLMF:27.13.E6
    0 references
    constraint
    | x | < 1 𝑥 1 {\displaystyle{\displaystyle|x|<1}}
    0 references
    Symbols used
    alternative notation
    Defining formula
    ϑ ⁡ ( x ) = θ 3 ⁡ ( 0 , x ) a-theta-function 𝑥 Jacobi-theta 3 0 𝑥 {\displaystyle{\displaystyle\vartheta\left(\NVar{x}\right)=\theta_{3}\left(0,x% \right)}}
    xml-id
    C27.S13.E4.m2abdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q8098&oldid=47691"