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:18.21.E12 - MaRDI portal

DLMF:18.21.E12 (Q6562)

From MaRDI portal
No description defined
Language Label Description Also known as
English
DLMF:18.21.E12
No description defined

    Statements

    DLMF defining formula
    lim ϕ → 0 ⁡ P n ( 1 2 ⁢ α + 1 2 ) ⁡ ( - ( 2 ⁢ ϕ ) - 1 ⁢ x ; ϕ ) = L n ( α ) ⁡ ( x ) . subscript → italic-ϕ 0 Meixner-Pollaczek-polynomial-P 1 2 𝛼 1 2 𝑛 superscript 2 italic-ϕ 1 𝑥 italic-ϕ Laguerre-polynomial-L 𝛼 𝑛 𝑥 {\displaystyle{\displaystyle\lim_{\phi\to 0}P^{(\frac{1}{2}\alpha+\frac{1}{2})% }_{n}\left(-(2\phi)^{-1}x;\phi\right)=L^{(\alpha)}_{n}\left(x\right).}}
    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.m2aadec
    0 references
    Meixner–Pollaczek polynomial
    DLMF defining formula
    P n ( λ ) ⁡ ( x ; ϕ ) Meixner-Pollaczek-polynomial-P 𝜆 𝑛 𝑥 italic-ϕ {\displaystyle{\displaystyle P^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x};% \NVar{\phi}\right)}}
    xml-id
    C18.S19.Px3.p1.m2abdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1kdec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1kdec
    0 references

    Identifiers

     
    Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Item:Q6562&oldid=24174951"
    Powered by MediaWiki