DLMF:28.28.E46 (Q8477)

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DLMF:28.28.E46
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    Statements

    Defining formula
    γ ^ n , m = 1 2 ⁢ π ⁢ ∫ 0 2 ⁢ π se n ′ ⁡ ( t , h 2 ) ⁢ ce m ⁡ ( t , h 2 ) ⁢ d t = ( - 1 ) p + 1 ⁢ 4 i ⁢ π ⁢ se n ′ ⁡ ( 0 , h 2 ) ⁢ ce m ⁡ ( 0 , h 2 ) Dsc 1 ⁡ ( n , m , 0 ) . subscript ^ 𝛾 𝑛 𝑚 1 2 𝜋 superscript subscript 0 2 𝜋 diffop Mathieu-se 𝑛 1 𝑡 superscript ℎ 2 Mathieu-ce 𝑚 𝑡 superscript ℎ 2 𝑡 superscript 1 𝑝 1 4 imaginary-unit 𝜋 diffop Mathieu-se 𝑛 1 0 superscript ℎ 2 Mathieu-ce 𝑚 0 superscript ℎ 2 Mathieu-Dsc 1 𝑛 𝑚 0 {\displaystyle{\displaystyle\widehat{\gamma}_{n,m}=\dfrac{1}{2\pi}\int_{0}^{2% \pi}\mathrm{se}_{n}'\left(t,h^{2}\right)\mathrm{ce}_{m}\left(t,h^{2}\right)% \mathrm{d}t=(-1)^{p+1}\dfrac{4}{\mathrm{i}\pi}\dfrac{\mathrm{se}_{n}'\left(0,h% ^{2}\right)\mathrm{ce}_{m}\left(0,h^{2}\right)}{\mathrm{Dsc}_{1}\left(n,m,0% \right)}.}}
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    DLMF id
    DLMF:28.28.E46
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