DLMF:18.12.E7 (Q5649)

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DLMF:18.12.E7
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    Statements

    Defining formula
    1 - z 2 1 - 2 ⁢ x ⁢ z + z 2 = 1 + 2 ⁢ ∑ n = 1 ∞ T n ⁡ ( x ) ⁢ z n , 1 superscript 𝑧 2 1 2 𝑥 𝑧 superscript 𝑧 2 1 2 superscript subscript 𝑛 1 Chebyshev-polynomial-first-kind-T 𝑛 𝑥 superscript 𝑧 𝑛 {\displaystyle{\displaystyle\frac{1-z^{2}}{1-2xz+z^{2}}=1+2\sum_{n=1}^{\infty}% T_{n}\left(x\right)z^{n},}}
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    DLMF id
    DLMF:18.12.E7
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    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
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