DLMF:23.22.E1 (Q7388)

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DLMF:23.22.E1
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    Statements

    Defining formula
    2 ⁢ ω 1 ⁢ M ⁢ ( 1 , k ′ ) = - 2 ⁢ i ⁢ ω 3 ⁢ M ⁢ ( 1 , k ) = π 3 ⁢ c ⁢ ( 2 + k 2 ⁢ k ′ 2 ) ⁢ ( k ′ 2 - k 2 ) d ⁢ ( 1 - k 2 ⁢ k ′ 2 ) , 2 subscript 𝜔 1 𝑀 1 superscript 𝑘 ′ 2 𝑖 subscript 𝜔 3 𝑀 1 𝑘 𝜋 3 𝑐 2 superscript 𝑘 2 superscript superscript 𝑘 ′ 2 superscript superscript 𝑘 ′ 2 superscript 𝑘 2 𝑑 1 superscript 𝑘 2 superscript superscript 𝑘 ′ 2 {\displaystyle{\displaystyle 2\omega_{1}M(1,k^{\prime})=-2i\omega_{3}M(1,k)=% \frac{\pi}{3}\sqrt{\frac{c(2+k^{2}{k^{\prime}}^{2})({k^{\prime}}^{2}-k^{2})}{d% (1-k^{2}{k^{\prime}}^{2})}},}}
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    DLMF id
    DLMF:23.22.E1
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    comment
    Warning: Falling back to standard tex;
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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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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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    Q12049
    Defining formula
    ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}}
    xml-id
    C23.S1.XMD8.m1dec
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    Q12109
    Defining formula
    M ⁢ ( j , k ) 𝑀 𝑗 𝑘 {\displaystyle{\displaystyle M(j,k)}}
    xml-id
    C23.S22.XMD4.m1dec
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    Q12062
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C23.S6.XMD3.m1dec
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    Q12070
    Defining formula
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C23.S6.XMD4.m1dec
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