DLMF:18.33.E10 (Q6017)

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DLMF:18.33.E10
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    z - n ϕ 2 n ( z ) = A n p n ( 1 2 ( z + z - 1 ) ) + B n ( z - z - 1 ) q n - 1 ( 1 2 ( z + z - 1 ) ) , superscript 𝑧 𝑛 subscript italic-ϕ 2 𝑛 𝑧 subscript 𝐴 𝑛 subscript 𝑝 𝑛 1 2 𝑧 superscript 𝑧 1 subscript 𝐵 𝑛 𝑧 superscript 𝑧 1 subscript 𝑞 𝑛 1 1 2 𝑧 superscript 𝑧 1 {\displaystyle{\displaystyle z^{-n}\phi_{2n}(z)={A_{n}p_{n}\left(\tfrac{1}{2}(% z+z^{-1})\right)+B_{n}(z-z^{-1})q_{n-1}\left(\tfrac{1}{2}(z+z^{-1})\right)},}}
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    Warning: Falling back to standard tex;
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C18.S1.XMD2.m1hdec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C18.S1.XMD6.m1hdec
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    ϕ n ( z ) subscript italic-ϕ 𝑛 𝑧 {\displaystyle{\displaystyle\phi_{n}(z)}}
    C18.S33.XMD1.m1hdec
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    q n ( x ) subscript 𝑞 𝑛 𝑥 {\displaystyle{\displaystyle q_{n}(x)}}
    C18.S33.XMD2.m1adec
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    p n ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}}
    C18.S33.XMD3.m1adec
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    A n subscript 𝐴 𝑛 {\displaystyle{\displaystyle A_{n}}}
    C18.S33.XMD4.m1dec
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    B n subscript 𝐵 𝑛 {\displaystyle{\displaystyle B_{n}}}
    C18.S33.XMD5.m1dec
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