DLMF:4.6.E7 (Q1633)

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DLMF:4.6.E7
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    Statements

    DLMF defining formula
    ( 1 + z ) a = 1 + a 1 ! ⁢ z + a ⁢ ( a - 1 ) 2 ! ⁢ z 2 + a ⁢ ( a - 1 ) ⁢ ( a - 2 ) 3 ! ⁢ z 3 + ⋯ , superscript 1 𝑧 𝑎 1 𝑎 1 𝑧 𝑎 𝑎 1 2 superscript 𝑧 2 𝑎 𝑎 1 𝑎 2 3 superscript 𝑧 3 ⋯ {\displaystyle{\displaystyle(1+z)^{a}=1+\frac{a}{1!}z+\frac{a(a-1)}{2!}z^{2}+% \frac{a(a-1)(a-2)}{3!}z^{3}+\cdots,}}
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    comment
    Warning: Falling back to standard tex;
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    Symbols used
    Q10729
    DLMF defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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    real or complex constant
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C4.S1.XMD4.m1adec
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    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1fdec
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