DLMF:18.9.E10 (Q5606)

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DLMF:18.9.E10
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    Statements

    Defining formula
    ( 1 - x 2 ) ⁢ U n ⁡ ( x ) = - 1 2 ⁢ ( T n + 2 ⁡ ( x ) - T n ⁡ ( x ) ) . 1 superscript 𝑥 2 Chebyshev-polynomial-second-kind-U 𝑛 𝑥 1 2 Chebyshev-polynomial-first-kind-T 𝑛 2 𝑥 Chebyshev-polynomial-first-kind-T 𝑛 𝑥 {\displaystyle{\displaystyle(1-x^{2})U_{n}\left(x\right)=-\tfrac{1}{2}\left(T_% {n+2}\left(x\right)-T_{n}\left(x\right)\right).}}
    0 references
    DLMF id
    DLMF:18.9.E10
    0 references
    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.m2abdec
    0 references
    Q11661
    Defining formula
    U n ⁡ ( x ) Chebyshev-polynomial-second-kind-U 𝑛 𝑥 {\displaystyle{\displaystyle U_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r5.m2abdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1jdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1idec
    0 references
     
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