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:18.27.E15 - MaRDI portal

DLMF:18.27.E15 (Q6662)

From MaRDI portal





No description defined
Language Label Description Also known as
English
DLMF:18.27.E15
No description defined

    Statements

    DLMF defining formula
    L n ( α ) ⁡ ( x ; q ) = ( q α + 1 ; q ) n ( q ; q ) n ⁢ ϕ 1 1 ⁡ ( q - n q α + 1 ; q , - x ⁢ q n + α + 1 ) . q-Laguerre-polynomial-L 𝛼 𝑛 𝑥 𝑞 q-Pochhammer-symbol superscript 𝑞 𝛼 1 𝑞 𝑛 q-Pochhammer-symbol 𝑞 𝑞 𝑛 q-hypergeometric-rphis 1 1 superscript 𝑞 𝑛 superscript 𝑞 𝛼 1 𝑞 𝑥 superscript 𝑞 𝑛 𝛼 1 {\displaystyle{\displaystyle L^{(\alpha)}_{n}\left(x;q\right)=\frac{\left(q^{% \alpha+1};q\right)_{n}}{\left(q;q\right)_{n}}{{}_{1}\phi_{1}}\left({q^{-n}% \atop q^{\alpha+1}};q,-xq^{n+\alpha+1}\right).}}
    0 references
    Symbols used
    Q11269
    DLMF defining formula
    ( a ; q ) n q-Pochhammer-symbol 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m2aadec
    0 references
    basic hypergeometric (or $$q$$ -hypergeometric) function
    DLMF defining formula
    ϕ s r + 1 ⁡ ( a 0 , … , a r ; b 1 , … , b s ; q , z ) q-hypergeometric-rphis 𝑟 1 𝑠 subscript 𝑎 0 … subscript 𝑎 𝑟 subscript 𝑏 1 … subscript 𝑏 𝑠 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{r+1}}\phi_{\NVar{s}}}\left(\NVar{a_{0},% \dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}
    xml-id
    C17.S4.E1.m2acdec
    0 references
    real variable
    DLMF defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C18.S1.XMD3.m1mdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1jdec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1jdec
    0 references

    Identifiers

     
    Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Item:Q6662&oldid=24174193"
    Powered by MediaWiki