DLMF:18.7.E16 (Q5584): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11660 / rank
 
Normal rank
Property / Symbols used: Q11660 / qualifier
 
test:

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.m2ajdec

Revision as of 14:20, 2 January 2020

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DLMF:18.7.E16
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    Statements

    C 2 n + 1 ( λ ) ( x ) = ( λ ) n + 1 ( 1 2 ) n + 1 x P n ( λ - 1 2 , 1 2 ) ( 2 x 2 - 1 ) . ultraspherical-Gegenbauer-polynomial 𝜆 2 𝑛 1 𝑥 Pochhammer 𝜆 𝑛 1 Pochhammer 1 2 𝑛 1 𝑥 Jacobi-polynomial-P 𝜆 1 2 1 2 𝑛 2 superscript 𝑥 2 1 {\displaystyle{\displaystyle C^{(\lambda)}_{2n+1}\left(x\right)=\frac{{\left(% \lambda\right)_{n+1}}}{{\left(\frac{1}{2}\right)_{n+1}}}xP^{(\lambda-\frac{1}{% 2},\frac{1}{2})}_{n}\left(2x^{2}-1\right).}}
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    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)}}
    C18.S3.T1.t1.r2.m2ajdec
    0 references