DLMF:18.27.E6 (Q5957): Difference between revisions

From DRMF
Jump to navigation Jump to search
Newer edit →
‎Created a new Item: Wikidata Toolkit example test item creation
 
‎Changed an Item: Wikidata Toolkit example test statement addition
Property / Symbols defined
 
Property / Symbols defined: big $$q$$ -Jacobi polynomial / rank
 
Normal rank

Revision as of 16:21, 30 December 2019

No description defined
Language Label Description Also known as
English
DLMF:18.27.E6
No description defined

    Statements

    Defining formula
    P n ( α , β ) ⁡ ( x ; c , d ; q ) = c n ⁢ q - ( α + 1 ) ⁢ n ⁢ ( q α + 1 , - q α + 1 ⁢ c - 1 ⁢ d ; q ) n ( q , - q ; q ) n ⁢ P n ⁡ ( q α + 1 ⁢ c - 1 ⁢ x ; q α , q β , - q α ⁢ c - 1 ⁢ d ; q ) . big-q-Jacobi-polynomial-P-type-2 𝛼 𝛽 𝑛 𝑥 𝑐 𝑑 𝑞 superscript 𝑐 𝑛 superscript 𝑞 𝛼 1 𝑛 q-multiple-Pochhammer superscript 𝑞 𝛼 1 superscript 𝑞 𝛼 1 superscript 𝑐 1 𝑑 𝑞 𝑛 q-multiple-Pochhammer 𝑞 𝑞 𝑞 𝑛 q-Jacobi-polynomial-P 𝑛 superscript 𝑞 𝛼 1 superscript 𝑐 1 𝑥 superscript 𝑞 𝛼 superscript 𝑞 𝛽 superscript 𝑞 𝛼 superscript 𝑐 1 𝑑 𝑞 {\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}\left(x;c,d;q\right)=\frac{% c^{n}q^{-(\alpha+1)n}\left(q^{\alpha+1},-q^{\alpha+1}c^{-1}d;q\right)_{n}}{% \left(q,-q;q\right)_{n}}\*P_{n}\left(q^{\alpha+1}c^{-1}x;q^{\alpha},q^{\beta},% -q^{\alpha}c^{-1}d;q\right).}}
    0 references
    DLMF id
    DLMF:18.27.E6
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5957&oldid=17213"