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DLMF:27.13.E4 - MaRDI portal

DLMF:27.13.E4 (Q8789)

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DLMF:27.13.E4
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    Statements

    DLMF defining formula
    ϑ ⁡ ( x ) = 1 + 2 ⁢ ∑ m = 1 ∞ x m 2 , a-theta-function 𝑥 1 2 superscript subscript 𝑚 1 superscript 𝑥 superscript 𝑚 2 {\displaystyle{\displaystyle\vartheta\left(x\right)=1+2\sum_{m=1}^{\infty}x^{m% ^{2}},}}
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    constraint
    | x | < 1 𝑥 1 {\displaystyle{\displaystyle|x|<1}}
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    Symbols used
    Q11948
    DLMF defining formula
    θ j ⁡ ( z , q ) Jacobi-theta 𝑗 𝑧 𝑞 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z},\NVar{q}\right)}}
    xml-id
    C20.S2.SS1.m2adec
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    positive integer
    DLMF defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C27.S1.XMD3.m1adec
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    real number
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C27.S1.XMD6.m1bdec
    0 references

    Identifiers

     
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