DLMF:18.9.E7 (Q5603): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q11475 / rank
 
Normal rank
Property / Symbols used: Q11475 / qualifier
 
Defining formula:

C n ( λ ) ( x ) ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 {\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}% \right)}}

\ultrasphpoly{\NVar{\lambda}}{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q11475 / qualifier
 
xml-id: C18.S3.T1.t1.r3.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.m1gdec
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.m1fdec

Latest revision as of 15:23, 2 January 2020

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DLMF:18.9.E7
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    Statements

    ( n + λ ) C n ( λ ) ( x ) = λ ( C n ( λ + 1 ) ( x ) - C n - 2 ( λ + 1 ) ( x ) ) , 𝑛 𝜆 ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 𝜆 ultraspherical-Gegenbauer-polynomial 𝜆 1 𝑛 𝑥 ultraspherical-Gegenbauer-polynomial 𝜆 1 𝑛 2 𝑥 {\displaystyle{\displaystyle(n+\lambda)C^{(\lambda)}_{n}\left(x\right)=\lambda% \left(C^{(\lambda+1)}_{n}\left(x\right)-C^{(\lambda+1)}_{n-2}\left(x\right)% \right),}}
    0 references
    DLMF:18.9.E7
    0 references
    C n ( λ ) ( x ) ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 {\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    C18.S3.T1.t1.r3.m2aadec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C18.S1.XMD6.m1gdec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C18.S2.XMD3.m1fdec
    0 references