DLMF:2.4.E4 (Q757)

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DLMF:2.4.E4
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    Statements

    Defining formula
    Q ⁢ ( z ) ∼ ∑ s = 0 ∞ Γ ⁡ ( s + λ μ ) ⁢ a s z ( s + λ ) / μ , asymptotic-expansion 𝑄 𝑧 superscript subscript 𝑠 0 Euler-Gamma 𝑠 𝜆 𝜇 subscript 𝑎 𝑠 superscript 𝑧 𝑠 𝜆 𝜇 {\displaystyle{\displaystyle Q(z)\sim\sum_{s=0}^{\infty}\Gamma\left(\frac{s+% \lambda}{\mu}\right)\frac{a_{s}}{z^{(s+\lambda)/\mu}},}}
    0 references
    DLMF id
    DLMF:2.4.E4
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    constraint
    z → ∞ → 𝑧 {\displaystyle{\displaystyle z\to\infty}}
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    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aadec
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    Q10971
    Defining formula
    λ 𝜆 {\displaystyle{\displaystyle\lambda}}
    xml-id
    C2.S4.XMD1.m1adec
    0 references
    Q10972
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C2.S4.XMD11.m1adec
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    Q10974
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C2.S4.XMD2.m1adec
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    Q10975
    Defining formula
    Q ⁢ ( z ) 𝑄 𝑧 {\displaystyle{\displaystyle Q(z)}}
    xml-id
    C2.S4.XMD6.m1bdec
    0 references
     
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