DLMF:18.9.E8 (Q5604): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
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.m1gdec

Latest revision as of 15:23, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:18.9.E8
No description defined

    Statements

    Defining formula
    4 ⁢ λ ⁢ ( n + λ + 1 ) ⁢ ( 1 - x 2 ) ⁢ C n ( λ + 1 ) ⁡ ( x ) = - ( n + 1 ) ⁢ ( n + 2 ) ⁢ C n + 2 ( λ ) ⁡ ( x ) + ( n + 2 ⁢ λ ) ⁢ ( n + 2 ⁢ λ + 1 ) ⁢ C n ( λ ) ⁡ ( x ) . 4 𝜆 𝑛 𝜆 1 1 superscript 𝑥 2 ultraspherical-Gegenbauer-polynomial 𝜆 1 𝑛 𝑥 𝑛 1 𝑛 2 ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 2 𝑥 𝑛 2 𝜆 𝑛 2 𝜆 1 ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 {\displaystyle{\displaystyle 4\lambda(n+\lambda+1)(1-x^{2})C^{(\lambda+1)}_{n}% \left(x\right)=-(n+1)(n+2)C^{(\lambda)}_{n+2}\left(x\right)+(n+2\lambda)(n+2% \lambda+1)C^{(\lambda)}_{n}\left(x\right).}}
    0 references
    DLMF id
    DLMF:18.9.E8
    0 references
    Symbols used
    Q11475
    Defining formula
    C n ( λ ) ⁡ ( x ) ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 {\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    xml-id
    C18.S3.T1.t1.r3.m2abdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1hdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1gdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5604&oldid=57249"