DLMF:28.10.E9 (Q8288)

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DLMF:28.10.E9
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    0 π / 2 J 0 ( 2 q ( cos 2 τ - sin 2 ζ ) ) ce 2 n ( τ , q ) d τ = w II ( 1 2 π ; a 2 n ( q ) , q ) ce 2 n ( ζ , q ) , superscript subscript 0 𝜋 2 Bessel-J 0 2 𝑞 2 𝜏 2 𝜁 Mathieu-ce 2 𝑛 𝜏 𝑞 𝜏 subscript 𝑤 II 1 2 𝜋 Mathieu-eigenvalue-a 2 𝑛 𝑞 𝑞 Mathieu-ce 2 𝑛 𝜁 𝑞 {\displaystyle{\displaystyle\int_{0}^{\ifrac{\pi}{2}}J_{0}\left(2\sqrt{q({\cos% ^{2}}\tau-{\sin^{2}}\zeta)}\right)\mathrm{ce}_{2n}\left(\tau,q\right)\mathrm{d% }\tau=w_{\mbox{\tiny II}}(\tfrac{1}{2}\pi;a_{2n}\left(q\right),q)\mathrm{ce}_{% 2n}\left(\zeta,q\right),}}
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    DLMF:28.10.E9
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