DLMF:8.8.E12 (Q2544): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11324 / rank
 
Normal rank
Property / Symbols used: Q11324 / qualifier
 
test:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11324 / qualifier
 
xml-id: C8.S1.XMD3.m1kdec
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.m1edec

Latest revision as of 12:49, 2 January 2020

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DLMF:8.8.E12
No description defined

    Statements

    test
    Q ⁡ ( a + n , z ) = Q ⁡ ( a , z ) + z a ⁢ e - z ⁢ ∑ k = 0 n - 1 z k Γ ⁡ ( a + k + 1 ) . incomplete-gamma-Q 𝑎 𝑛 𝑧 incomplete-gamma-Q 𝑎 𝑧 superscript 𝑧 𝑎 superscript 𝑒 𝑧 superscript subscript 𝑘 0 𝑛 1 superscript 𝑧 𝑘 Euler-Gamma 𝑎 𝑘 1 {\displaystyle{\displaystyle Q\left(a+n,z\right)=Q\left(a,z\right)+z^{a}e^{-z}% \sum_{k=0}^{n-1}\frac{z^{k}}{\Gamma\left(a+k+1\right)}.}}
    0 references
    DLMF id
    DLMF:8.8.E12
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2ahdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ajdec
    0 references
    Q11326
    test
    Q ⁡ ( a , z ) incomplete-gamma-Q 𝑎 𝑧 {\displaystyle{\displaystyle Q\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E4.m2aadec
    0 references
    Q11323
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1kdec
    0 references
    Q11324
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1kdec
    0 references
    Q11330
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C8.S1.XMD5.m1edec
    0 references
     
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