DLMF:1.4.E12 (Q91)

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DLMF:1.4.E12
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    Statements

    Defining formula
    ( f ⁢ g ) ( n ) = f ( n ) ⁢ g + ( n 1 ) ⁢ f ( n - 1 ) ⁢ g ′ + … + ( n k ) ⁢ f ( n - k ) ⁢ g ( k ) + … + f ⁢ g ( n ) . superscript 𝑓 𝑔 𝑛 superscript 𝑓 𝑛 𝑔 binomial 𝑛 1 superscript 𝑓 𝑛 1 superscript 𝑔 ′ … binomial 𝑛 𝑘 superscript 𝑓 𝑛 𝑘 superscript 𝑔 𝑘 … 𝑓 superscript 𝑔 𝑛 {\displaystyle{\displaystyle(fg)^{(n)}=f^{(n)}g+\genfrac{(}{)}{0.0pt}{}{n}{1}f% ^{(n-1)}g^{\prime}+\dots+\genfrac{(}{)}{0.0pt}{}{n}{k}f^{(n-k)}g^{(k)}+\dots+% fg^{(n)}.}}
    0 references
    DLMF id
    DLMF:1.4.E12
    0 references
    Symbols used
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1adec
    0 references
    Q10756
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C1.S1.XMD4.m1dec
    0 references
    Q10757
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1adec
    0 references
     
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