DLMF:17.2.E43 (Q5333)

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DLMF:17.2.E43
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    Statements

    Defining formula
    𝒟 q ⁢ ( f ⁢ ( z ) ⁢ g ⁢ ( z ) ) = g ⁢ ( z ) ⁢ f [ 1 ] ⁢ ( z ) + f ⁢ ( z ⁢ q ) ⁢ g [ 1 ] ⁢ ( z ) . subscript 𝒟 𝑞 𝑓 𝑧 𝑔 𝑧 𝑔 𝑧 superscript 𝑓 delimited-[] 1 𝑧 𝑓 𝑧 𝑞 superscript 𝑔 delimited-[] 1 𝑧 {\displaystyle{\displaystyle\mathcal{D}_{q}(f(z)g(z))=g(z)f^{[1]}(z)+f(zq)g^{[% 1]}(z).}}
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    DLMF id
    DLMF:17.2.E43
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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.m1aodec
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    Q11718
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C17.S1.XMD7.m1fdec
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    $$q$$ -differential operator (locally)
    Defining formula
    𝒟 q subscript 𝒟 𝑞 {\displaystyle{\displaystyle\mathcal{D}_{q}}}
    xml-id
    C17.S2.XMD1.m1bdec
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