DLMF:8.7.E6 (Q2532): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11333 / rank
 
Normal rank
Property / Symbols used: Q11333 / qualifier
 
test:

L n ( α ) ⁡ ( x ) Laguerre-polynomial-L 𝛼 𝑛 𝑥 {\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}% \right)}}

\LaguerrepolyL[\NVar{\alpha}]{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q11333 / qualifier
 
xml-id: C18.S3.T1.t1.r12.m2adec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2aedec
Property / Symbols used
 
Property / Symbols used: incomplete gamma function / rank
 
Normal rank
Property / Symbols used: incomplete gamma function / qualifier
 
test:

Γ ⁡ ( a , z ) incomplete-Gamma 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}

\incGamma@{\NVar{a}}{\NVar{z}}
Property / Symbols used: incomplete gamma function / qualifier
 
xml-id: C8.S2.E2.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11332 / rank
 
Normal rank
Property / Symbols used: Q11332 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11332 / qualifier
 
xml-id: C8.S1.XMD1.m1bdec
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.m1edec
Property / Symbols used
 
Property / Symbols used: Q11329 / rank
 
Normal rank
Property / Symbols used: Q11329 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11329 / qualifier
 
xml-id: C8.S1.XMD6.m1cdec

Latest revision as of 12:46, 2 January 2020

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DLMF:8.7.E6
No description defined

    Statements

    test
    Γ ⁡ ( a , x ) = x a ⁢ e - x ⁢ ∑ n = 0 ∞ L n ( a ) ⁡ ( x ) n + 1 , incomplete-Gamma 𝑎 𝑥 superscript 𝑥 𝑎 superscript 𝑒 𝑥 superscript subscript 𝑛 0 Laguerre-polynomial-L 𝑎 𝑛 𝑥 𝑛 1 {\displaystyle{\displaystyle\Gamma\left(a,x\right)=x^{a}e^{-x}\sum_{n=0}^{% \infty}\frac{L^{(a)}_{n}\left(x\right)}{n+1},}}
    0 references
    DLMF id
    DLMF:8.7.E6
    0 references
    constraint
    x > 0 𝑥 0 {\displaystyle{\displaystyle x>0}}
    0 references
    Symbols used
    Q11333
    test
    L n ( α ) ⁡ ( x ) Laguerre-polynomial-L 𝛼 𝑛 𝑥 {\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    xml-id
    C18.S3.T1.t1.r12.m2adec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
    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.m2abdec
    0 references
    Q11332
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C8.S1.XMD1.m1bdec
    0 references
    Q11324
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1edec
    0 references
    Q11329
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C8.S1.XMD6.m1cdec
    0 references
     
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