DLMF:18.7.E18 (Q5586): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1qdec

Latest revision as of 15:21, 2 January 2020

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DLMF:18.7.E18
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    Statements

    Defining formula
    T 2 ⁢ n + 1 ⁡ ( x ) = x ⁢ W n ⁡ ( 2 ⁢ x 2 - 1 ) . Chebyshev-polynomial-first-kind-T 2 𝑛 1 𝑥 𝑥 Chebyshev-polynomial-fourth-kind-W 𝑛 2 superscript 𝑥 2 1 {\displaystyle{\displaystyle T_{2n+1}\left(x\right)=xW_{n}\left(2x^{2}-1\right% ).}}
    0 references
    DLMF id
    DLMF:18.7.E18
    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
    Q11746
    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.m2aadec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1qdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1qdec
    0 references
     
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