DLMF:10.51#Ex6 (Q3740)

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DLMF:10.51#Ex6
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    Statements

    Defining formula
    ( 1 z ⁢ d d z ) m ⁡ ( z - n ⁢ f n ⁢ ( z ) ) = ( - 1 ) m ⁢ z - n - m ⁢ f n + m ⁢ ( z ) , superscript 1 𝑧 derivative 𝑧 𝑚 superscript 𝑧 𝑛 subscript 𝑓 𝑛 𝑧 superscript 1 𝑚 superscript 𝑧 𝑛 𝑚 subscript 𝑓 𝑛 𝑚 𝑧 {\displaystyle{\displaystyle\left(\frac{1}{z}\frac{\mathrm{d}}{\mathrm{d}z}% \right)^{m}(z^{-n}f_{n}(z))=(-1)^{m}z^{-n-m}f_{n+m}(z),}}
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    DLMF id
    DLMF:10.51#Ex6
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    constraint
    m = 0 , 1 , … . 𝑚 0 1 … {\displaystyle{\displaystyle m=0,1,\dots.}}
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