DLMF:28.28.E23 (Q8449)

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DLMF:28.28.E23
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    Statements

    Defining formula
    2 π ⁢ ∫ 0 π 𝒞 2 ⁢ ℓ + 2 ( j ) ⁢ ( 2 ⁢ h ⁢ R ) ⁢ sin ⁡ ( ( 2 ⁢ ℓ + 2 ) ⁢ ϕ ) ⁢ se 2 ⁢ m + 2 ⁡ ( t , h 2 ) ⁢ d t = ( - 1 ) ℓ + m ⁢ B 2 ⁢ ℓ + 2 2 ⁢ m + 2 ⁢ ( h 2 ) ⁢ Ms 2 ⁢ m + 2 ( j ) ⁡ ( z , h ) . 2 𝜋 superscript subscript 0 𝜋 subscript superscript 𝒞 𝑗 2 ℓ 2 2 ℎ 𝑅 2 ℓ 2 italic-ϕ Mathieu-se 2 𝑚 2 𝑡 superscript ℎ 2 𝑡 superscript 1 ℓ 𝑚 subscript superscript 𝐵 2 𝑚 2 2 ℓ 2 superscript ℎ 2 modified-Mathieu-Ms 𝑗 2 𝑚 2 𝑧 ℎ {\displaystyle{\displaystyle\dfrac{2}{\pi}\int_{0}^{\pi}\mathcal{C}^{(j)}_{2% \ell+2}(2hR)\sin\left((2\ell+2)\phi\right)\mathrm{se}_{2m+2}\left(t,h^{2}% \right)\mathrm{d}t=(-1)^{\ell+m}B^{2m+2}_{2\ell+2}(h^{2}){\mathrm{Ms}^{(j)}_{2% m+2}}\left(z,h\right).}}
    0 references
    DLMF id
    DLMF:28.28.E23
    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.m8addec
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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.m2asdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aqdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aqdec
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    radial Mathieu function
    Defining formula
    Ms n ( j ) ⁡ ( z , h ) modified-Mathieu-Ms 𝑗 𝑛 𝑧 ℎ {\displaystyle{\displaystyle{\mathrm{Ms}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z% },\NVar{h}\right)}}
    xml-id
    C28.S20.E16.m2addec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2acdec
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    Q12284
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1edec
    0 references
     
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