DLMF:8.11.E7 (Q2578): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10931 / rank
 
Normal rank
Property / Symbols used: Q10931 / qualifier
 
Defining formula:

∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}

\asympexp
Property / Symbols used: Q10931 / qualifier
 
xml-id: C2.S1.SS3.p1.m11aadec

Revision as of 13:54, 2 January 2020

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DLMF:8.11.E7
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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.E7
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    constraint
    | ph ⁡ a | ≤ 3 ⁢ π 2 - δ phase 𝑎 3 𝜋 2 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}a|\leq\frac{3\pi}{2}-\delta}}
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    λ > 1 𝜆 1 {\displaystyle{\displaystyle\lambda>1}}
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    | ph ⁡ a | ≤ 3 ⁢ π 2 - δ ph 𝑎 3 𝜋 2 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}a|\leq\frac{3\pi}{2}-\delta}}
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    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aadec
    0 references
     
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