DLMF:28.10.E6 (Q8285)

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DLMF:28.10.E6
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    Statements

    Defining formula
    2 π ⁢ ∫ 0 π / 2 sin ⁡ z ⁢ sin ⁡ t ⁢ cos ⁡ ( 2 ⁢ h ⁢ cos ⁡ z ⁢ cos ⁡ t ) ⁢ se 2 ⁢ n + 1 ⁡ ( t , h 2 ) ⁢ d t = B 1 2 ⁢ n + 1 ⁢ ( h 2 ) 2 ⁢ se 2 ⁢ n + 1 ⁡ ( 1 2 ⁢ π , h 2 ) ⁢ se 2 ⁢ n + 1 ⁡ ( z , h 2 ) , 2 𝜋 superscript subscript 0 𝜋 2 𝑧 𝑡 2 ℎ 𝑧 𝑡 Mathieu-se 2 𝑛 1 𝑡 superscript ℎ 2 𝑡 superscript subscript 𝐵 1 2 𝑛 1 superscript ℎ 2 2 Mathieu-se 2 𝑛 1 1 2 𝜋 superscript ℎ 2 Mathieu-se 2 𝑛 1 𝑧 superscript ℎ 2 {\displaystyle{\displaystyle\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\sin z\sin t% \cos\left(2h\cos z\cos t\right)\mathrm{se}_{2n+1}\left(t,h^{2}\right)\mathrm{d% }t=\frac{B_{1}^{2n+1}(h^{2})}{2\mathrm{se}_{2n+1}\left(\frac{1}{2}\pi,h^{2}% \right)}\mathrm{se}_{2n+1}\left(z,h^{2}\right),}}
    0 references
    DLMF id
    DLMF:28.10.E6
    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.m8aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2acdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aedec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aedec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2addec
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    Q12294
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C28.S1.XMD11.m1edec
    0 references
    Q12279
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C28.S1.XMD2.m1edec
    0 references
    Q12272
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1edec
    0 references
    Q12288
    Defining formula
    B m ⁢ ( q ) subscript 𝐵 𝑚 𝑞 {\displaystyle{\displaystyle B_{m}(q)}}
    xml-id
    C28.S4.XMD2.m1adec
    0 references
     
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