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),}}
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    DLMF id
    DLMF:13.7.E5
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