DLMF:18.7.E5 (Q5573): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11660 / rank
 
Normal rank
Property / Symbols used: Q11660 / qualifier
 
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)}}

\JacobipolyP{\NVar{\alpha}}{\NVar{\beta}}{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q11660 / qualifier
 
xml-id: C18.S3.T1.t1.r2.m2addec

Revision as of 15:19, 2 January 2020

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DLMF:18.7.E5
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    Statements

    Defining formula
    V n ⁡ ( x ) = ( 2 ⁢ n + 1 ) ⁢ P n ( 1 2 , - 1 2 ) ⁡ ( x ) / P n ( 1 2 , - 1 2 ) ⁡ ( 1 ) , Chebyshev-polynomial-third-kind-V 𝑛 𝑥 2 𝑛 1 Jacobi-polynomial-P 1 2 1 2 𝑛 𝑥 Jacobi-polynomial-P 1 2 1 2 𝑛 1 {\displaystyle{\displaystyle V_{n}\left(x\right)=\ifrac{(2n+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.E5
    0 references
    Symbols used
    Q11745
    Defining formula
    V n ⁡ ( x ) Chebyshev-polynomial-third-kind-V 𝑛 𝑥 {\displaystyle{\displaystyle V_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r6.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.m2addec
    0 references
     
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