DLMF:18.9.E18 (Q5614): Difference between revisions

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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.m2agdec

Revision as of 15:24, 2 January 2020

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DLMF:18.9.E18
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    Statements

    Defining formula
    ( 2 ⁢ n + α + β + 2 ) ⁢ ( 1 - x 2 ) ⁢ d d x ⁡ P n ( α , β ) ⁡ ( x ) = ( n + α + β + 1 ) ⁢ ( α - β + ( 2 ⁢ n + α + β + 2 ) ⁢ x ) ⁢ P n ( α , β ) ⁡ ( x ) - 2 ⁢ ( n + 1 ) ⁢ ( n + α + β + 1 ) ⁢ P n + 1 ( α , β ) ⁡ ( x ) . 2 𝑛 𝛼 𝛽 2 1 superscript 𝑥 2 derivative 𝑥 Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 𝑛 𝛼 𝛽 1 𝛼 𝛽 2 𝑛 𝛼 𝛽 2 𝑥 Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 2 𝑛 1 𝑛 𝛼 𝛽 1 Jacobi-polynomial-P 𝛼 𝛽 𝑛 1 𝑥 {\displaystyle{\displaystyle(2n+\alpha+\beta+2)(1-x^{2})\frac{\mathrm{d}}{% \mathrm{d}x}P^{(\alpha,\beta)}_{n}\left(x\right)=(n+\alpha+\beta+1)\left(% \alpha-\beta+(2n+\alpha+\beta+2)x\right)P^{(\alpha,\beta)}_{n}\left(x\right)-2% (n+1)(n+\alpha+\beta+1)P^{(\alpha,\beta)}_{n+1}\left(x\right).}}
    0 references
    DLMF id
    DLMF:18.9.E18
    0 references
    Symbols used
    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.m2agdec
    0 references
     
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