DLMF:27.13.E6 (Q8098)

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DLMF:27.13.E6
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    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
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    constraint
    | x | < 1 𝑥 1 {\displaystyle{\displaystyle|x|<1}}
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    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
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    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1cdec
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    Q12237
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C27.S1.XMD6.m1ddec
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    Q12265
    Defining formula
    δ j ⁢ ( n ) subscript 𝛿 𝑗 𝑛 {\displaystyle{\displaystyle\delta_{j}(n)}}
    xml-id
    C27.S13.XMD5.m1dec
    0 references
     
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