DLMF:18.22.E5 (Q5872)

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DLMF:18.22.E5
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    Statements

    Defining formula
    ( a + i ⁢ x ) ⁢ q n ⁢ ( x ) = A ~ n ⁢ q n + 1 ⁢ ( x ) - ( A ~ n + C ~ n ) ⁢ q n ⁢ ( x ) + C ~ n ⁢ q n - 1 ⁢ ( x ) , 𝑎 imaginary-unit 𝑥 subscript 𝑞 𝑛 𝑥 subscript ~ 𝐴 𝑛 subscript 𝑞 𝑛 1 𝑥 subscript ~ 𝐴 𝑛 subscript ~ 𝐶 𝑛 subscript 𝑞 𝑛 𝑥 subscript ~ 𝐶 𝑛 subscript 𝑞 𝑛 1 𝑥 {\displaystyle{\displaystyle(a+\mathrm{i}x)q_{n}(x)=\tilde{A}_{n}q_{n+1}(x)-% \bigl{(}\tilde{A}_{n}+\tilde{C}_{n}\bigr{)}q_{n}(x)+\tilde{C}_{n}q_{n-1}(x),}}
    0 references
    DLMF id
    DLMF:18.22.E5
    0 references
    Symbols used
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    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.m1ddec
    0 references
    Q11772
    Defining formula
    A ~ n subscript ~ 𝐴 𝑛 {\displaystyle{\displaystyle\tilde{A}_{n}}}
    xml-id
    C18.S22.XMD5.m1dec
    0 references
    Q11773
    Defining formula
    C ~ n subscript ~ 𝐶 𝑛 {\displaystyle{\displaystyle\tilde{C}_{n}}}
    xml-id
    C18.S22.XMD6.m1dec
    0 references
     
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