DLMF:18.26.E6 (Q5936)

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DLMF:18.26.E6
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    Statements

    Defining formula
    lim t → ∞ ⁡ W n ⁡ ( ( x + t ) 2 ; a - i ⁢ t , b - i ⁢ t , a ¯ + i ⁢ t , b ¯ + i ⁢ t ) ( - 2 ⁢ t ) n ⁢ n ! = p n ⁡ ( x ; a , b , a ¯ , b ¯ ) . subscript → 𝑡 Wilson-polynomial-W 𝑛 superscript 𝑥 𝑡 2 𝑎 𝑖 𝑡 𝑏 𝑖 𝑡 𝑎 𝑖 𝑡 𝑏 𝑖 𝑡 superscript 2 𝑡 𝑛 𝑛 continuous-Hahn-polynomial-p 𝑛 𝑥 𝑎 𝑏 𝑎 𝑏 {\displaystyle{\displaystyle\lim_{t\to\infty}\frac{W_{n}\left((x+t)^{2};a-it,b% -it,\overline{a}+it,\overline{b}+it\right)}{(-2t)^{n}n!}=p_{n}\left(x;a,b,% \overline{a},\overline{b}\right).}}
    0 references
    DLMF id
    DLMF:18.26.E6
    0 references
    Symbols used
    Q11783
    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.m2abdec
    0 references
    complex conjugate
    Defining formula
    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    xml-id
    C1.S9.E11.m2adec
    0 references
    Q11763
    Defining formula
    p n ⁡ ( x ; a , b , a ¯ , missing ) continuous-Hahn-polynomial-p 𝑛 𝑥 𝑎 𝑏 𝑎 missing {\displaystyle{\displaystyle p_{\NVar{n}}\left(\NVar{x};\NVar{a},\NVar{b},% \NVar{\overline{a}},\NVar{missing}\right)\)\@add@PDF@RDFa@triples\end{document}}}
    xml-id
    C18.S19.Px2.p1.m4adec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1edec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1adec
    0 references
     
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