DLMF:28.22.E8 (Q8373)

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DLMF:28.22.E8
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    Statements

    Defining formula
    g o , 2 ⁢ m + 2 ⁢ ( h ) = ( - 1 ) m + 1 ⁢ 2 π ⁢ se 2 ⁢ m + 2 ′ ⁡ ( 1 2 ⁢ π , h 2 ) h 2 ⁢ B 2 2 ⁢ m + 2 ⁢ ( h 2 ) , subscript 𝑔 𝑜 2 𝑚 2 ℎ superscript 1 𝑚 1 2 𝜋 diffop Mathieu-se 2 𝑚 2 1 1 2 𝜋 superscript ℎ 2 superscript ℎ 2 superscript subscript 𝐵 2 2 𝑚 2 superscript ℎ 2 {\displaystyle{\displaystyle g_{\mathit{o},2m+2}(h)=(-1)^{m+1}\sqrt{\dfrac{2}{% \pi}}\dfrac{\mathrm{se}_{2m+2}'\left(\frac{1}{2}\pi,h^{2}\right)}{h^{2}B_{2}^{% 2m+2}(h^{2})},}}
    0 references
    DLMF id
    DLMF:28.22.E8
    0 references
    Symbols used
    Q12286
    Defining formula
    se n ⁡ ( z , q ) Mathieu-se 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{se}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S2.SS6.p1.m8acdec
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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.m2agdec
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    Q12284
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1gdec
    0 references
    Q12294
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C28.S1.XMD11.m1gdec
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    Q12302
    Defining formula
    g e , n ⁢ ( h ) subscript 𝑔 𝑒 𝑛 ℎ {\displaystyle{\displaystyle g_{\mathit{e},n}(h)}}
    xml-id
    C28.S22.XMD1.m1gdec
    0 references
     
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