DLMF:18.22.E17 (Q5887)

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DLMF:18.22.E17
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    Statements

    Defining formula
    A ⁢ ( x ) ⁢ p n ⁢ ( x + i ) - ( A ⁢ ( x ) + C ⁢ ( x ) ) ⁢ p n ⁢ ( x ) + C ⁢ ( x ) ⁢ p n ⁢ ( x - i ) + 2 ⁢ n ⁢ sin ⁡ ϕ ⁢ p n ⁢ ( x ) = 0 , 𝐴 𝑥 subscript 𝑝 𝑛 𝑥 𝑖 𝐴 𝑥 𝐶 𝑥 subscript 𝑝 𝑛 𝑥 𝐶 𝑥 subscript 𝑝 𝑛 𝑥 𝑖 2 𝑛 italic-ϕ subscript 𝑝 𝑛 𝑥 0 {\displaystyle{\displaystyle A(x)p_{n}(x+i)-\left(A(x)+C(x)\right)p_{n}(x)+C(x% )p_{n}(x-i)+2n\sin\phi\,p_{n}(x)=0,}}
    0 references
    DLMF id
    DLMF:18.22.E17
    0 references
    Symbols used
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2addec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1pdec
    0 references
    Q11731
    Defining formula
    p n ⁢ ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}}
    xml-id
    C18.S1.XMD9.m1ldec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1pdec
    0 references
    Q11781
    Defining formula
    A ⁢ ( x ) 𝐴 𝑥 {\displaystyle{\displaystyle A(x)}}
    xml-id
    C18.S22.XMD14.m1dec
    0 references
    Q11782
    Defining formula
    C ⁢ ( x ) 𝐶 𝑥 {\displaystyle{\displaystyle C(x)}}
    xml-id
    C18.S22.XMD15.m1dec
    0 references
     
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