DLMF:18.9.E18 (Q5614)

From DRMF
Revision as of 16:06, 29 December 2019 by Admin (talk | contribs) (‎Created a new Item: Wikidata Toolkit example test item creation)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:18.9.E18
No description defined

    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
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5614&oldid=11613"