DLMF:18.9.E12 (Q5608): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q11746 / rank
 
Normal rank
Property / Symbols used: Q11746 / qualifier
 
Defining formula:

W n ( x ) Chebyshev-polynomial-fourth-kind-W 𝑛 𝑥 {\displaystyle{\displaystyle W_{\NVar{n}}\left(\NVar{x}\right)}}

\ChebyshevpolyW{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q11746 / qualifier
 
xml-id: C18.S3.T1.t1.r7.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1ldec
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.m1kdec

Latest revision as of 15:23, 2 January 2020

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DLMF:18.9.E12
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    Statements

    T n + 1 ( x ) + T n ( x ) = ( 1 + x ) W n ( x ) . Chebyshev-polynomial-first-kind-T 𝑛 1 𝑥 Chebyshev-polynomial-first-kind-T 𝑛 𝑥 1 𝑥 Chebyshev-polynomial-fourth-kind-W 𝑛 𝑥 {\displaystyle{\displaystyle T_{n+1}\left(x\right)+T_{n}\left(x\right)=(1+x)W_% {n}\left(x\right).}}
    0 references
    DLMF:18.9.E12
    0 references
    T n ( x ) Chebyshev-polynomial-first-kind-T 𝑛 𝑥 {\displaystyle{\displaystyle T_{\NVar{n}}\left(\NVar{x}\right)}}
    C18.S3.T1.t1.r4.m2addec
    0 references
    W n ( x ) Chebyshev-polynomial-fourth-kind-W 𝑛 𝑥 {\displaystyle{\displaystyle W_{\NVar{n}}\left(\NVar{x}\right)}}
    C18.S3.T1.t1.r7.m2aadec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C18.S1.XMD6.m1ldec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C18.S2.XMD3.m1kdec
    0 references