DLMF:18.18.E33 (Q5823)

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DLMF:18.18.E33
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    Statements

    Defining formula
    2 ⁢ ∑ ℓ = 0 n T 2 ⁢ ℓ + 1 ⁡ ( x ) = U 2 ⁢ n + 1 ⁡ ( x ) . 2 superscript subscript ℓ 0 𝑛 Chebyshev-polynomial-first-kind-T 2 ℓ 1 𝑥 Chebyshev-polynomial-second-kind-U 2 𝑛 1 𝑥 {\displaystyle{\displaystyle 2\sum_{\ell=0}^{n}T_{2\ell+1}\left(x\right)=U_{2n% +1}\left(x\right).}}
    0 references
    DLMF id
    DLMF:18.18.E33
    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.m2acdec
    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
     
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