DLMF:10.43#Ex4 (Q3617)

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DLMF:10.43#Ex4
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    Statements

    test
    ∫ e ± z ⁢ z - ν ⁢ 𝒵 ν ⁡ ( z ) ⁢ d z = e ± z ⁢ z - ν + 1 1 - 2 ⁢ ν ⁢ ( 𝒵 ν ⁡ ( z ) ∓ 𝒵 ν - 1 ⁡ ( z ) ) , superscript 𝑒 plus-or-minus 𝑧 superscript 𝑧 𝜈 modified-cylinder-function 𝜈 𝑧 𝑧 superscript 𝑒 plus-or-minus 𝑧 superscript 𝑧 𝜈 1 1 2 𝜈 minus-or-plus modified-cylinder-function 𝜈 𝑧 modified-cylinder-function 𝜈 1 𝑧 {\displaystyle{\displaystyle\int e^{\pm z}z^{-\nu}\mathscr{Z}_{\nu}\left(z% \right)\mathrm{d}z=\frac{e^{\pm z}z^{-\nu+1}}{1-2\nu}\left(\mathscr{Z}_{\nu}% \left(z\right)\mp\mathscr{Z}_{\nu-1}\left(z\right)\right),}}
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    DLMF id
    DLMF:10.43#Ex4
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    constraint
    ν ≠ 1 2 𝜈 1 2 {\displaystyle{\displaystyle\nu\neq\tfrac{1}{2}}}
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