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DLMF:10.6#Ex10 - MaRDI portal

DLMF:10.6#Ex10 (Q3740)

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DLMF:10.6#Ex10
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    DLMF defining formula
    ( 1 z ⁢ d d z ) k ⁡ ( z - ν ⁢ 𝒞 ν ⁡ ( z ) ) = ( - 1 ) k ⁢ z - ν - k ⁢ 𝒞 ν + k ⁡ ( z ) . superscript 1 𝑧 derivative 𝑧 𝑘 superscript 𝑧 𝜈 cylinder-function 𝜈 𝑧 superscript 1 𝑘 superscript 𝑧 𝜈 𝑘 cylinder-function 𝜈 𝑘 𝑧 {\displaystyle{\displaystyle\left(\frac{1}{z}\frac{\mathrm{d}}{\mathrm{d}z}% \right)^{k}(z^{-\nu}\mathscr{C}_{\nu}\left(z\right))=(-1)^{k}z^{-\nu-k}% \mathscr{C}_{\nu+k}\left(z\right).}}
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