Deprecated: $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372
DLMF:8.7.E6 - MaRDI portal

DLMF:8.7.E6 (Q3230)

From MaRDI portal





No description defined
Language Label Description Also known as
English
DLMF:8.7.E6
No description defined

    Statements

    DLMF defining formula
    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
    constraint
    x > 0 𝑥 0 {\displaystyle{\displaystyle x>0}}
    0 references
    Symbols used
    Laguerre (or generalized Laguerre) polynomial
    DLMF defining formula
    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
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
    0 references
    incomplete gamma function
    DLMF defining formula
    Γ ⁡ ( a , z ) incomplete-Gamma 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E2.m2abdec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C8.S1.XMD1.m1bdec
    0 references
    parameter
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1edec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C8.S1.XMD6.m1cdec
    0 references

    Identifiers

     
    Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Item:Q3230&oldid=24165953"
    Powered by MediaWiki