DLMF:18.12.E7 (Q5649)

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DLMF:18.12.E7
No description defined

    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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    Symbols used
    Q11207
    Defining formula
    T n ⁡ ( x ) Chebyshev-polynomial-first-kind-T 𝑛 𝑥 {\displaystyle{\displaystyle T_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r4.m2adec
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    Q11750
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C18.S1.XMD2.m1fdec
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    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1fdec
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    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1edec
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