DLMF:18.28.E9 (Q5984): 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: $$q^{-1}$$ -Al-Salam–Chihara polynomial / rank
 
Normal rank

Revision as of 16:22, 30 December 2019

No description defined
Language Label Description Also known as
English
DLMF:18.28.E9
No description defined

    Statements

    Defining formula
    Q n ⁡ ( 1 2 ⁢ ( a ⁢ q - y + a - 1 ⁢ q y ) ; a , b | q - 1 ) = ( - 1 ) n ⁢ b n ⁢ q - 1 2 ⁢ n ⁢ ( n - 1 ) ⁢ ( ( a ⁢ b ) - 1 ; q ) n ⁢ ϕ 1 3 ⁡ ( q - n , q - y , a - 2 ⁢ q y ( a ⁢ b ) - 1 ; q , q n ⁢ a ⁢ b - 1 ) . q-inverse-AlSalam-Chihara-polynomial-Q 𝑛 1 2 𝑎 superscript 𝑞 𝑦 superscript 𝑎 1 superscript 𝑞 𝑦 𝑎 𝑏 superscript 𝑞 1 superscript 1 𝑛 superscript 𝑏 𝑛 superscript 𝑞 1 2 𝑛 𝑛 1 q-Pochhammer-symbol superscript 𝑎 𝑏 1 𝑞 𝑛 q-hypergeometric-rphis 3 1 superscript 𝑞 𝑛 superscript 𝑞 𝑦 superscript 𝑎 2 superscript 𝑞 𝑦 superscript 𝑎 𝑏 1 𝑞 superscript 𝑞 𝑛 𝑎 superscript 𝑏 1 {\displaystyle{\displaystyle Q_{n}\left(\tfrac{1}{2}(aq^{-y}+a^{-1}q^{y});a,b% \,|\,q^{-1}\right)=(-1)^{n}b^{n}q^{-\frac{1}{2}n(n-1)}\*\left((ab)^{-1};q% \right)_{n}{{}_{3}\phi_{1}}\left({q^{-n},q^{-y},a^{-2}q^{y}\atop(ab)^{-1}};q,q% ^{n}ab^{-1}\right).}}
    0 references
    DLMF id
    DLMF:18.28.E9
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5984&oldid=17222"