DLMF:11.10.E33 (Q4055)

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DLMF:11.10.E33
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    𝐄 ν - 1 ( z ) + 𝐄 ν + 1 ( z ) = 2 ν z 𝐄 ν ( z ) - 2 π z ( 1 - cos ( π ν ) ) . Weber-E 𝜈 1 𝑧 Weber-E 𝜈 1 𝑧 2 𝜈 𝑧 Weber-E 𝜈 𝑧 2 𝜋 𝑧 1 𝜋 𝜈 {\displaystyle{\displaystyle\mathbf{E}_{\nu-1}\left(z\right)+\mathbf{E}_{\nu+1% }\left(z\right)=\frac{2\nu}{z}\mathbf{E}_{\nu}\left(z\right)-\frac{2}{\pi z}(1% -\cos\left(\pi\nu\right)).}}
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