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:18.14.E8 - MaRDI portal

DLMF:18.14.E8 (Q6368)

From MaRDI portal
No description defined
Language Label Description Also known as
English
DLMF:18.14.E8
No description defined

    Statements

    DLMF defining formula
    e - 1 2 ⁢ x ⁢ | L n ( α ) ⁡ ( x ) | ≤ L n ( α ) ⁡ ( 0 ) = ( α + 1 ) n n ! , superscript 𝑒 1 2 𝑥 Laguerre-polynomial-L 𝛼 𝑛 𝑥 Laguerre-polynomial-L 𝛼 𝑛 0 Pochhammer 𝛼 1 𝑛 𝑛 {\displaystyle{\displaystyle e^{-\frac{1}{2}x}\left|L^{(\alpha)}_{n}\left(x% \right)\right|\leq L^{(\alpha)}_{n}\left(0\right)=\frac{{\left(\alpha+1\right)% _{n}}}{n!},}}
    0 references
    constraint
    α ≥ 0 𝛼 0 {\displaystyle{\displaystyle\alpha\geq 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
    Q10733
    DLMF defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1aedec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    Q10729
    DLMF defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5afdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1edec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1gdec
    0 references

    Identifiers

     
    Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Item:Q6368&oldid=24174591"
    Powered by MediaWiki