DLMF:3.11.E11 (Q1452): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11207 / rank
 
Normal rank
Property / Symbols used: Q11207 / qualifier
 
Defining formula:

T n ⁡ ( x ) Chebyshev-polynomial-first-kind-T 𝑛 𝑥 {\displaystyle{\displaystyle T_{\NVar{n}}\left(\NVar{x}\right)}}

\ChebyshevpolyT{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q11207 / qualifier
 
xml-id: C18.S3.T1.t1.r4.m2addec
Property / Symbols used
 
Property / Symbols used: coefficients (locally) / rank
 
Normal rank
Property / Symbols used: coefficients (locally) / qualifier
 
Defining formula:

c n subscript 𝑐 𝑛 {\displaystyle{\displaystyle c_{n}}}

c_{n}
Property / Symbols used: coefficients (locally) / qualifier
 
xml-id: C3.S11.XMD4.m1adec

Latest revision as of 17:58, 1 January 2020

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DLMF:3.11.E11
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    Statements

    Defining formula
    f ⁢ ( x ) = ∑ ′ n = 0 ′ ∞ ′ ⁢ c n ⁢ T n ⁡ ( x ) , 𝑓 𝑥 superscript subscript superscript ′ 𝑛 0 subscript 𝑐 𝑛 Chebyshev-polynomial-first-kind-T 𝑛 𝑥 {\displaystyle{\displaystyle f(x)=\sideset{}{{}^{\prime}}{\sum}_{n=0}^{\infty}% c_{n}T_{n}\left(x\right),}}
    0 references
    DLMF id
    DLMF:3.11.E11
    0 references
    constraint
    - 1 ≤ x ≤ 1 1 𝑥 1 {\displaystyle{\displaystyle-1\leq x\leq 1}}
    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.m2addec
    0 references
    coefficients (locally)
    Defining formula
    c n subscript 𝑐 𝑛 {\displaystyle{\displaystyle c_{n}}}
    xml-id
    C3.S11.XMD4.m1adec
    0 references
     
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