DLMF:1.9.E63 (Q345)

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DLMF:1.9.E63
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    Statements

    Defining formula
    f ( m ) ⁢ ( z ) = ∑ n = 0 ∞ ( n + 1 ) m ⁢ a n + m ⁢ ( z - z 0 ) n , superscript 𝑓 𝑚 𝑧 superscript subscript 𝑛 0 Pochhammer 𝑛 1 𝑚 subscript 𝑎 𝑛 𝑚 superscript 𝑧 subscript 𝑧 0 𝑛 {\displaystyle{\displaystyle f^{(m)}(z)=\sum_{n=0}^{\infty}{\left(n+1\right)_{% m}}a_{n+m}(z-z_{0})^{n},}}
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    DLMF id
    DLMF:1.9.E63
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    constraint
    | z - z 0 | < R 𝑧 subscript 𝑧 0 𝑅 {\displaystyle{\displaystyle\left|z-z_{0}\right|<R}}
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    | z - z 0 | < R 𝑧 subscript 𝑧 0 𝑅 {\displaystyle{\displaystyle\left|z-z_{0}\right|<R}}
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    m = 0 , 1 , 2 , … 𝑚 0 1 2 … {\displaystyle{\displaystyle m=0,1,2,\dots}}
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    Symbols used
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
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    Q10760
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C1.S1.XMD1.m1ajdec
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