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DLMF:10.61#Ex12 - MaRDI portal

DLMF:10.61#Ex12 (Q4502)

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DLMF:10.61#Ex12
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    bei - 1 2 ( x 2 ) = - 2 - 3 4 π x ( e x cos ( x + π 8 ) + e - x cos ( x - π 8 ) ) . Kelvin-bei 1 2 𝑥 2 superscript 2 3 4 𝜋 𝑥 superscript 𝑒 𝑥 𝑥 𝜋 8 superscript 𝑒 𝑥 𝑥 𝜋 8 {\displaystyle{\displaystyle\operatorname{bei}_{-\frac{1}{2}}\left(x\sqrt{2}% \right)=-\frac{2^{-\frac{3}{4}}}{\sqrt{\pi x}}\left(e^{x}\cos\left(x+\frac{\pi% }{8}\right)+e^{-x}\cos\left(x-\frac{\pi}{8}\right)\right).}}
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