DLMF:10.22#Ex3 (Q3375)

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DLMF:10.22#Ex3
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    Statements

    test
    ∫ e i ⁢ z ⁢ z ν ⁢ 𝒞 ν ⁡ ( z ) ⁢ d z = e i ⁢ z ⁢ z ν + 1 2 ⁢ ν + 1 ⁢ ( 𝒞 ν ⁡ ( z ) - i ⁢ 𝒞 ν + 1 ⁡ ( z ) ) , superscript 𝑒 𝑖 𝑧 superscript 𝑧 𝜈 cylinder-function 𝜈 𝑧 𝑧 superscript 𝑒 𝑖 𝑧 superscript 𝑧 𝜈 1 2 𝜈 1 cylinder-function 𝜈 𝑧 𝑖 cylinder-function 𝜈 1 𝑧 {\displaystyle{\displaystyle\int e^{iz}z^{\nu}\mathscr{C}_{\nu}\left(z\right)% \mathrm{d}z=\frac{e^{iz}z^{\nu+1}}{2\nu+1}(\mathscr{C}_{\nu}\left(z\right)-i% \mathscr{C}_{\nu+1}\left(z\right)),}}
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    DLMF id
    DLMF:10.22#Ex3
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    constraint
    ν ≠ - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\nu\neq-\tfrac{1}{2}}}
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