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

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Property / Symbols used
 
Property / Symbols used: Q11330 / rank
 
Normal rank
Property / Symbols used: Q11330 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11330 / qualifier
 
xml-id: C8.S1.XMD5.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11343 / rank
 
Normal rank
Property / Symbols used: Q11343 / qualifier
 
test:

δ 𝛿 {\displaystyle{\displaystyle\delta}}

\delta
Property / Symbols used: Q11343 / qualifier
 
xml-id: C8.S1.XMD7.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11344 / rank
 
Normal rank
Property / Symbols used: Q11344 / qualifier
 
test:

λ 𝜆 {\displaystyle{\displaystyle\lambda}}

\lambda
Property / Symbols used: Q11344 / qualifier
 
xml-id: C8.S11.XMD3.m1adec

Latest revision as of 12:54, 2 January 2020

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DLMF:8.11.E7
No description defined

    Statements

    test
    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}},}}
    0 references
    DLMF id
    DLMF:8.11.E7
    0 references
    constraint
    | ph ⁡ a | ≤ 3 ⁢ π 2 - δ phase 𝑎 3 𝜋 2 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}a|\leq\frac{3\pi}{2}-\delta}}
    0 references
    λ > 1 𝜆 1 {\displaystyle{\displaystyle\lambda>1}}
    0 references
    | ph ⁡ a | ≤ 3 ⁢ π 2 - δ ph 𝑎 3 𝜋 2 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}a|\leq\frac{3\pi}{2}-\delta}}
    0 references
    Symbols used
    Q10931
    test
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2addec
    0 references
    incomplete gamma function
    test
    Γ ⁡ ( a , z ) incomplete-Gamma 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E2.m2aadec
    0 references
    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1acdec
    0 references
    Q11332
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C8.S1.XMD1.m1adec
    0 references
    Q11323
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1edec
    0 references
    Q11324
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1fdec
    0 references
    Q11330
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C8.S1.XMD5.m1ddec
    0 references
    Q11343
    test
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C8.S1.XMD7.m1cdec
    0 references
    Q11344
    test
    λ 𝜆 {\displaystyle{\displaystyle\lambda}}
    xml-id
    C8.S11.XMD3.m1adec
    0 references
     
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