DLMF:28.10.E8 (Q8287)

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DLMF:28.10.E8
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    Statements

    Defining formula
    2 π ⁢ ∫ 0 π / 2 cos ⁡ z ⁢ cos ⁡ t ⁢ sinh ⁡ ( 2 ⁢ h ⁢ sin ⁡ z ⁢ sin ⁡ t ) ⁢ se 2 ⁢ n + 2 ⁡ ( t , h 2 ) ⁢ d t = h ⁢ B 2 2 ⁢ n + 2 ⁢ ( h 2 ) 2 ⁢ se 2 ⁢ n + 2 ′ ⁡ ( 0 , h 2 ) ⁢ se 2 ⁢ n + 2 ⁡ ( z , h 2 ) . 2 𝜋 superscript subscript 0 𝜋 2 𝑧 𝑡 2 ℎ 𝑧 𝑡 Mathieu-se 2 𝑛 2 𝑡 superscript ℎ 2 𝑡 ℎ superscript subscript 𝐵 2 2 𝑛 2 superscript ℎ 2 2 diffop Mathieu-se 2 𝑛 2 1 0 superscript ℎ 2 Mathieu-se 2 𝑛 2 𝑧 superscript ℎ 2 {\displaystyle{\displaystyle\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\cos z\cos t% \sinh\left(2h\sin z\sin t\right)\mathrm{se}_{2n+2}\left(t,h^{2}\right)\mathrm{% d}t=\frac{hB_{2}^{2n+2}(h^{2})}{2\mathrm{se}_{2n+2}'\left(0,h^{2}\right)}% \mathrm{se}_{2n+2}\left(z,h^{2}\right).}}
    0 references
    DLMF id
    DLMF:28.10.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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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aedec
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