DLMF:20.13.E4 (Q6854)

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DLMF:20.13.E4
No description defined

    Statements

    Defining formula
    π 4 ⁢ α ⁢ t ⁢ ∑ n = - ∞ ∞ e - ( n ⁢ π + z ) 2 / ( 4 ⁢ α ⁢ t ) = θ 3 ⁡ ( z | i ⁢ 4 ⁢ α ⁢ t / π ) , 𝜋 4 𝛼 𝑡 superscript subscript 𝑛 superscript 𝑒 superscript 𝑛 𝜋 𝑧 2 4 𝛼 𝑡 Jacobi-theta-tau 3 𝑧 𝑖 4 𝛼 𝑡 𝜋 {\displaystyle{\displaystyle\sqrt{\frac{\pi}{4\alpha t}}\sum\limits_{n=-\infty% }^{\infty}e^{-(n\pi+z)^{2}/(4\alpha t)}=\theta_{3}\left(z\middle|i4\alpha t/% \pi\right),}}
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    DLMF id
    DLMF:20.13.E4
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    Symbols used
    Q11946
    Defining formula
    θ j ⁡ ( z | τ ) Jacobi-theta-tau 𝑗 𝑧 𝜏 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z}\middle|\NVar{\tau}% \right)}}
    xml-id
    C20.S2.SS1.m1adec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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    Q11947
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C20.S1.XMD2.m1dec
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    Q11957
    Defining formula
    t 𝑡 {\displaystyle{\displaystyle t}}
    xml-id
    C20.S13.XMD1.m1bdec
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    Q11958
    Defining formula
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C20.S13.XMD2.m1bdec
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    Q11956
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S13.XMD3.m1cdec
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