DLMF:18.23.E2 (Q5903)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:18.23.E2
No description defined

    Statements

    Defining formula
    F 0 2 ⁡ ( - x , - x + β + N + 1 - ; - z ) ⁢ F 0 2 ⁡ ( x - N , x + α + 1 - ; z ) = ∑ n = 0 N ( - N ) n ⁢ ( α + 1 ) n n ! ⁢ Q n ⁡ ( x ; α , β , N ) ⁢ z n , Gauss-hypergeometric-pFq 2 0 𝑥 𝑥 𝛽 𝑁 1 𝑧 Gauss-hypergeometric-pFq 2 0 𝑥 𝑁 𝑥 𝛼 1 𝑧 superscript subscript 𝑛 0 𝑁 Pochhammer 𝑁 𝑛 Pochhammer 𝛼 1 𝑛 𝑛 Hahn-polynomial-Q 𝑛 𝑥 𝛼 𝛽 𝑁 superscript 𝑧 𝑛 {\displaystyle{\displaystyle{{}_{2}F_{0}}\left({-x,-x+\beta+N+1\atop-};-z% \right)\*{{}_{2}F_{0}}\left({x-N,x+\alpha+1\atop-};z\right)=\sum_{n=0}^{N}% \frac{{\left(-N\right)_{n}}{\left(\alpha+1\right)_{n}}}{n!}Q_{n}\left(x;\alpha% ,\beta,N\right)z^{n},}}
    0 references
    DLMF id
    DLMF:18.23.E2
    0 references
    constraint
    x = 0 , 1 , … , N 𝑥 0 1 … 𝑁 {\displaystyle{\displaystyle x=0,1,\dots,N}}
    0 references
    Symbols used
    Q11125
    Defining formula
    F q p ⁡ ( a 1 , … , a p ; b 1 , … , b q ; z ) Gauss-hypergeometric-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}
    xml-id
    C16.S2.m1adec
    0 references
    Q11768
    Defining formula
    Q n ⁡ ( x ; α , β , N ) Hahn-polynomial-Q 𝑛 𝑥 𝛼 𝛽 𝑁 {\displaystyle{\displaystyle Q_{\NVar{n}}\left(\NVar{x};\NVar{\alpha},\NVar{% \beta},\NVar{N}\right)}}
    xml-id
    C18.S19.T1.t1.r2.m1aadec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1aadec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    Q11750
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C18.S1.XMD2.m1adec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1adec
    0 references
    Q11736
    Defining formula
    N 𝑁 {\displaystyle{\displaystyle N}}
    xml-id
    C18.S1.XMD7.m1adec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5903&oldid=33386"