DLMF:23.10.E15 (Q7313)

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DLMF:23.10.E15
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    Statements

    Defining formula
    A n = ( π 2 ⁢ G 2 ω 1 ) n 2 - 1 ⁢ q n ⁢ ( n - 1 ) / 2 i n - 1 ⁢ exp ⁡ ( - ( n - 1 ) ⁢ η 1 3 ⁢ ω 1 ⁢ ( ( 2 ⁢ n - 1 ) ⁢ ( ω 1 2 + ω 3 2 ) + 3 ⁢ ( n - 1 ) ⁢ ω 1 ⁢ ω 3 ) ) , subscript 𝐴 𝑛 superscript superscript 𝜋 2 superscript 𝐺 2 subscript 𝜔 1 superscript 𝑛 2 1 superscript 𝑞 𝑛 𝑛 1 2 superscript 𝑖 𝑛 1 𝑛 1 subscript 𝜂 1 3 subscript 𝜔 1 2 𝑛 1 superscript subscript 𝜔 1 2 superscript subscript 𝜔 3 2 3 𝑛 1 subscript 𝜔 1 subscript 𝜔 3 {\displaystyle{\displaystyle A_{n}=\left(\frac{\pi^{2}G^{2}}{\omega_{1}}\right% )^{n^{2}-1}\frac{q^{n(n-1)/2}}{i^{n-1}}\exp\left(-\frac{(n-1)\eta_{1}}{3\omega% _{1}}\left((2n-1)(\omega_{1}^{2}+\omega_{3}^{2})+3(n-1)\omega_{1}\omega_{3}% \right)\right),}}
    0 references
    DLMF id
    DLMF:23.10.E15
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.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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    Q12066
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C23.S1.XMD10.m1dec
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    Q12060
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C23.S1.XMD3.m1ddec
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    Q12049
    Defining formula
    ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}}
    xml-id
    C23.S1.XMD8.m1ddec
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    Q12079
    Defining formula
    A n subscript 𝐴 𝑛 {\displaystyle{\displaystyle A_{n}}}
    xml-id
    C23.S10.XMD2.m1bdec
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    Q12080
    Defining formula
    G 𝐺 {\displaystyle{\displaystyle G}}
    xml-id
    C23.S10.XMD3.m1dec
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    Q12059
    Defining formula
    η j subscript 𝜂 𝑗 {\displaystyle{\displaystyle\eta_{j}}}
    xml-id
    C23.S2.XMD6.m1bdec
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