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DLMF:18.26.E5 - MaRDI portal

DLMF:18.26.E5 (Q6631)

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DLMF:18.26.E5
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    Statements

    DLMF defining formula
    lim d → ∞ ⁡ W n ⁡ ( x ; a , b , c , d ) ( a + d ) n = S n ⁡ ( x ; a , b , c ) . subscript → 𝑑 Wilson-polynomial-W 𝑛 𝑥 𝑎 𝑏 𝑐 𝑑 Pochhammer 𝑎 𝑑 𝑛 continuous-dual-Hahn-S 𝑛 𝑥 𝑎 𝑏 𝑐 {\displaystyle{\displaystyle\lim_{d\to\infty}\frac{W_{n}\left(x;a,b,c,d\right)% }{{\left(a+d\right)_{n}}}=S_{n}\left(x;a,b,c\right).}}
    0 references
    Symbols used
    Q10733
    DLMF defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1abdec
    0 references
    Wilson polynomial
    DLMF defining formula
    W n ⁡ ( x ; a , b , c , d ) Wilson-polynomial-W 𝑛 𝑥 𝑎 𝑏 𝑐 𝑑 {\displaystyle{\displaystyle W_{\NVar{n}}\left(\NVar{x};\NVar{a},\NVar{b},% \NVar{c},\NVar{d}\right)}}
    xml-id
    C18.S25.T1.t1.r2.m2aadec
    0 references
    continuous dual Hahn polynomial
    DLMF defining formula
    S n ⁡ ( x ; a , b , c ) continuous-dual-Hahn-S 𝑛 𝑥 𝑎 𝑏 𝑐 {\displaystyle{\displaystyle S_{\NVar{n}}\left(\NVar{x};\NVar{a},\NVar{b},% \NVar{c}\right)}}
    xml-id
    C18.S25.T1.t1.r3.m2aadec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1ddec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1dec
    0 references

    Identifiers

     
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