DLMF:18.22.E27 (Q5898)

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DLMF:18.22.E27
No description defined

    Statements

    Defining formula
    δ x ( p n ⁡ ( x ; a , b , a ¯ , b ¯ ) ) = ( n + 2 ⁢ ℜ ⁡ ( a + b ) - 1 ) ⁢ p n - 1 ⁡ ( x ; a + 1 2 , b + 1 2 , a ¯ + 1 2 , b ¯ + 1 2 ) , central-difference 𝑥 continuous-Hahn-polynomial-p 𝑛 𝑥 𝑎 𝑏 𝑎 𝑏 𝑛 2 𝑎 𝑏 1 continuous-Hahn-polynomial-p 𝑛 1 𝑥 𝑎 1 2 𝑏 1 2 𝑎 1 2 𝑏 1 2 {\displaystyle{\displaystyle\delta_{x}\left(p_{n}\left(x;a,b,\overline{a},% \overline{b}\right)\right)=(n+2\Re(a+b)-1)\*p_{n-1}\left(x;a+\tfrac{1}{2},b+% \tfrac{1}{2},\overline{a}+\tfrac{1}{2},\overline{b}+\tfrac{1}{2}\right),}}
    0 references
    DLMF id
    DLMF:18.22.E27
    0 references
    Symbols used
    Q11767
    Defining formula
    δ x central-difference 𝑥 {\displaystyle{\displaystyle\delta_{\NVar{x}}}}
    xml-id
    C18.S1.EGx3.m1adec
    0 references
    complex conjugate
    Defining formula
    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    xml-id
    C1.S9.E11.m2addec
    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.m4abdec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1abdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1ydec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1zdec
    0 references
     
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