DLMF:18.7.E4 (Q5572): Difference between revisions

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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.m1cdec

Latest revision as of 15:19, 2 January 2020

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DLMF:18.7.E4
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    Statements

    Defining formula
    U n ⁡ ( x ) = C n ( 1 ) ⁡ ( x ) = ( n + 1 ) ⁢ P n ( 1 2 , 1 2 ) ⁡ ( x ) / P n ( 1 2 , 1 2 ) ⁡ ( 1 ) , Chebyshev-polynomial-second-kind-U 𝑛 𝑥 ultraspherical-Gegenbauer-polynomial 1 𝑛 𝑥 𝑛 1 Jacobi-polynomial-P 1 2 1 2 𝑛 𝑥 Jacobi-polynomial-P 1 2 1 2 𝑛 1 {\displaystyle{\displaystyle U_{n}\left(x\right)=C^{(1)}_{n}\left(x\right)=% \ifrac{(n+1)P^{(\frac{1}{2},\frac{1}{2})}_{n}\left(x\right)}{P^{(\frac{1}{2},% \frac{1}{2})}_{n}\left(1\right)},}}
    0 references
    DLMF id
    DLMF:18.7.E4
    0 references
    Symbols used
    Q11661
    Defining formula
    U n ⁡ ( x ) Chebyshev-polynomial-second-kind-U 𝑛 𝑥 {\displaystyle{\displaystyle U_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r5.m2adec
    0 references
    Q11660
    Defining formula
    P n ( α , β ) ⁡ ( x ) Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 {\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r2.m2acdec
    0 references
    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.m1cdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1cdec
    0 references
     
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