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DLMF:18.9.E11 - MaRDI portal

DLMF:18.9.E11 (Q6304)

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DLMF:18.9.E11
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    Statements

    DLMF defining formula
    W n ⁡ ( x ) + W n - 1 ⁡ ( x ) = 2 ⁢ T n ⁡ ( x ) , Chebyshev-polynomial-fourth-kind-W 𝑛 𝑥 Chebyshev-polynomial-fourth-kind-W 𝑛 1 𝑥 2 Chebyshev-polynomial-first-kind-T 𝑛 𝑥 {\displaystyle{\displaystyle W_{n}\left(x\right)+W_{n-1}\left(x\right)=2T_{n}% \left(x\right),}}
    0 references
    Symbols used
    Chebyshev polynomial of the first kind
    DLMF 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
    Chebyshev polynomial of the fourth kind
    DLMF defining formula
    W n ⁡ ( x ) Chebyshev-polynomial-fourth-kind-W 𝑛 𝑥 {\displaystyle{\displaystyle W_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r7.m2adec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1kdec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1jdec
    0 references

    Identifiers

     
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