DLMF:27.13.E5 (Q8097)

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DLMF:27.13.E5
No description defined

    Statements

    Defining formula
    ( ϑ ⁡ ( x ) ) 2 = 1 + ∑ n = 1 ∞ r 2 ⁡ ( n ) ⁢ x n . superscript a-theta-function 𝑥 2 1 superscript subscript 𝑛 1 number-of-squares-R 2 𝑛 superscript 𝑥 𝑛 {\displaystyle{\displaystyle(\vartheta\left(x\right))^{2}=1+\sum_{n=1}^{\infty% }r_{2}\left(n\right)x^{n}.}}
    0 references
    DLMF id
    DLMF:27.13.E5
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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.m2aadec
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    Q12264
    Defining formula
    r k ⁡ ( n ) number-of-squares-R 𝑘 𝑛 {\displaystyle{\displaystyle r_{\NVar{k}}\left(\NVar{n}\right)}}
    xml-id
    C27.S13.SS4.p1.m3adec
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    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1bdec
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    Q12237
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C27.S1.XMD6.m1cdec
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