DLMF:28.28.E17 (Q8441)

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DLMF:28.28.E17
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    Statements

    Defining formula
    1 π ⁢ ∫ 0 π 𝒞 ν + 2 ⁢ s ( j ) ⁢ ( 2 ⁢ h ⁢ R ) ⁢ e - i ⁢ ( ν + 2 ⁢ s ) ⁢ ϕ ⁢ me ν ⁡ ( t , h 2 ) ⁢ d t = ( - 1 ) s ⁢ c 2 ⁢ s ν ⁢ ( h 2 ) ⁢ M ν ( j ) ⁡ ( z , h ) , 1 𝜋 superscript subscript 0 𝜋 subscript superscript 𝒞 𝑗 𝜈 2 𝑠 2 ℎ 𝑅 superscript 𝑒 imaginary-unit 𝜈 2 𝑠 italic-ϕ Mathieu-me 𝜈 𝑡 superscript ℎ 2 𝑡 superscript 1 𝑠 subscript superscript 𝑐 𝜈 2 𝑠 superscript ℎ 2 modified-Mathieu-M 𝑗 𝜈 𝑧 ℎ {\displaystyle{\displaystyle\dfrac{1}{\pi}\int_{0}^{\pi}\mathcal{C}^{(j)}_{\nu% +2s}(2hR)e^{-\mathrm{i}(\nu+2s)\phi}\mathrm{me}_{\nu}\left(t,h^{2}\right)% \mathrm{d}t=(-1)^{s}c^{\nu}_{2s}(h^{2}){\mathrm{M}^{(j)}_{\nu}}\left(z,h\right% ),}}
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    DLMF id
    DLMF:28.28.E17
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    constraint
    s ∈ ℤ 𝑠 {\displaystyle{\displaystyle s\in\mathbb{Z}}}
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