DLMF:17.2.E41 (Q5331)

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DLMF:17.2.E41
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    Statements

    Defining formula
    𝒟 q ⁢ f ⁢ ( z ) = { f ⁢ ( z ) - f ⁢ ( z ⁢ q ) ( 1 - q ) ⁢ z , z ≠ 0 , f ′ ⁢ ( 0 ) , z = 0 , subscript 𝒟 𝑞 𝑓 𝑧 cases 𝑓 𝑧 𝑓 𝑧 𝑞 1 𝑞 𝑧 𝑧 0 superscript 𝑓 ′ 0 𝑧 0 {\displaystyle{\displaystyle\mathcal{D}_{q}f(z)=\begin{cases}\dfrac{f(z)-f(zq)% }{(1-q)z},&z\neq 0,\\ f^{\prime}(0),&z=0,\end{cases}}}
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    DLMF id
    DLMF:17.2.E41
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    comment
    Warning: Falling back to standard tex;
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    Symbols used
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1amdec
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    Q11718
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C17.S1.XMD7.m1ddec
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