DLMF:18.18.E26 (Q5816): 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.m2afdec

Revision as of 01:26, 2 January 2020

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DLMF:18.18.E26
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    Statements

    Defining formula
    P n ( α , β ) ⁡ ( x ) P n ( α , β ) ⁡ ( 1 ) = ∑ ℓ = 0 n b n , ℓ ⁢ ( x + 1 ) ℓ . Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 Jacobi-polynomial-P 𝛼 𝛽 𝑛 1 superscript subscript ℓ 0 𝑛 subscript 𝑏 𝑛 ℓ superscript 𝑥 1 ℓ {\displaystyle{\displaystyle\frac{P^{(\alpha,\beta)}_{n}\left(x\right)}{P^{(% \alpha,\beta)}_{n}\left(1\right)}=\sum_{\ell=0}^{n}b_{n,\ell}(x+1)^{\ell}.}}
    0 references
    DLMF id
    DLMF:18.18.E26
    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.m2afdec
    0 references
     
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