DLMF:8.11.E6 (Q2577)

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DLMF:8.11.E6
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    Statements

    Defining formula
    γ ⁡ ( a , z ) ∼ - z a ⁢ e - z ⁢ ∑ k = 0 ∞ ( - a ) k ⁢ b k ⁢ ( λ ) ( z - a ) 2 ⁢ k + 1 , asymptotic-expansion incomplete-gamma 𝑎 𝑧 superscript 𝑧 𝑎 superscript 𝑒 𝑧 superscript subscript 𝑘 0 superscript 𝑎 𝑘 subscript 𝑏 𝑘 𝜆 superscript 𝑧 𝑎 2 𝑘 1 {\displaystyle{\displaystyle\gamma\left(a,z\right)\sim-z^{a}e^{-z}\sum_{k=0}^{% \infty}\frac{(-a)^{k}b_{k}(\lambda)}{(z-a)^{2k+1}},}}
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    DLMF id
    DLMF:8.11.E6
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    constraint
    | ph ⁡ a | ≤ π 2 - δ phase 𝑎 𝜋 2 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}a|\leq\frac{\pi}{2}-\delta}}
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    0 < λ < 1 0 𝜆 1 {\displaystyle{\displaystyle 0<\lambda<1}}
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    | ph ⁡ a | ≤ π 2 - δ ph 𝑎 𝜋 2 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}a|\leq\frac{\pi}{2}-\delta}}
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    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11adec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
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    incomplete gamma function
    Defining formula
    γ ⁡ ( a , z ) incomplete-gamma 𝑎 𝑧 {\displaystyle{\displaystyle\gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E1.m2aadec
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    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1abdec
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