DLMF:18.9.E11 (Q5607): Difference between revisions

From DRMF
Jump to navigation Jump to search
Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
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.m2acdec
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.m2adec
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.m1kdec
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.m1jdec

Latest revision as of 15:23, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:18.9.E11
No description defined

    Statements

    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
    DLMF:18.9.E11
    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.m2acdec
    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.m2adec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C18.S1.XMD6.m1kdec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C18.S2.XMD3.m1jdec
    0 references