DLMF:28.28.E43 (Q8474): Difference between revisions

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Revision as of 16:26, 30 December 2019

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DLMF:28.28.E43
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    β ^ n , m = 1 2 π 0 2 π sin t se n ( t , h 2 ) ce m ( t , h 2 ) d t = ( - 1 ) p 2 i π se n ( 0 , h 2 ) ce m ( 0 , h 2 ) h Dsc 1 ( n , m , 0 ) . subscript ^ 𝛽 𝑛 𝑚 1 2 𝜋 superscript subscript 0 2 𝜋 𝑡 Mathieu-se 𝑛 𝑡 superscript 2 Mathieu-ce 𝑚 𝑡 superscript 2 𝑡 superscript 1 𝑝 2 imaginary-unit 𝜋 diffop Mathieu-se 𝑛 1 0 superscript 2 Mathieu-ce 𝑚 0 superscript 2 Mathieu-Dsc 1 𝑛 𝑚 0 {\displaystyle{\displaystyle\widehat{\beta}_{n,m}=\dfrac{1}{2\pi}\int_{0}^{2% \pi}\sin t\mathrm{se}_{n}\left(t,h^{2}\right)\mathrm{ce}_{m}\left(t,h^{2}% \right)\mathrm{d}t=(-1)^{p}\dfrac{2}{\mathrm{i}\pi}\dfrac{\mathrm{se}_{n}'% \left(0,h^{2}\right)\mathrm{ce}_{m}\left(0,h^{2}\right)}{h\mathrm{Dsc}_{1}% \left(n,m,0\right)}.}}
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    DLMF:28.28.E43
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