DLMF:13.7.E5 (Q4413)

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DLMF:13.7.E5
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    Statements

    Defining formula
    | ε n ⁢ ( z ) | , β - 1 ⁢ | ε n ′ ⁢ ( z ) | ≤ 2 ⁢ α ⁢ C n ⁢ | ( a ) n ⁢ ( a - b + 1 ) n n ! ⁢ z a + n | ⁢ exp ⁡ ( 2 ⁢ α ⁢ ρ ⁢ C 1 | z | ) , subscript 𝜀 𝑛 𝑧 superscript 𝛽 1 superscript subscript 𝜀 𝑛 ′ 𝑧 2 𝛼 subscript 𝐶 𝑛 Pochhammer 𝑎 𝑛 Pochhammer 𝑎 𝑏 1 𝑛 𝑛 superscript 𝑧 𝑎 𝑛 2 𝛼 𝜌 subscript 𝐶 1 𝑧 {\displaystyle{\displaystyle\left|\varepsilon_{n}(z)\right|,~{}{}\beta^{-1}% \left|\varepsilon_{n}^{\prime}(z)\right|\leq 2\alpha C_{n}\left|\frac{{\left(a% \right)_{n}}{\left(a-b+1\right)_{n}}}{n!z^{a+n}}\right|\exp\left(\frac{2\alpha% \rho C_{1}}{|z|}\right),}}
    0 references
    DLMF id
    DLMF:13.7.E5
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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.m1addec
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    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5addec
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    Q11559
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1adec
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    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1cdec
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    coefficient (locally)
    Defining formula
    C n subscript 𝐶 𝑛 {\displaystyle{\displaystyle C_{n}}}
    xml-id
    C13.S7.XMD2.m1dec
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    Q11567
    Defining formula
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C13.S7.XMD6.m1dec
    0 references
    Q11568
    Defining formula
    β 𝛽 {\displaystyle{\displaystyle\beta}}
    xml-id
    C13.S7.XMD7.m1dec
    0 references
     
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