DLMF:18.27.E3 (Q5954): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11728 / rank
 
Normal rank
Property / Symbols used: Q11728 / qualifier
 
test:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q11728 / qualifier
 
xml-id: C18.S1.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11736 / rank
 
Normal rank
Property / Symbols used: Q11736 / qualifier
 
test:

N 𝑁 {\displaystyle{\displaystyle N}}

N
Property / Symbols used: Q11736 / qualifier
 
xml-id: C18.S1.XMD7.m1dec
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1bdec

Latest revision as of 00:47, 2 January 2020

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Language Label Description Also known as
English
DLMF:18.27.E3
No description defined

    Statements

    test
    Q n ⁢ ( x ) = Q n ⁡ ( x ; α , β , N ; q ) = ϕ 2 3 ⁡ ( q - n , α ⁢ β ⁢ q n + 1 , x α ⁢ q , q - N ; q , q ) , subscript 𝑄 𝑛 𝑥 q-Hahn-polynomial-Q 𝑛 𝑥 𝛼 𝛽 𝑁 𝑞 q-hypergeometric-rphis 3 2 superscript 𝑞 𝑛 𝛼 𝛽 superscript 𝑞 𝑛 1 𝑥 𝛼 𝑞 superscript 𝑞 𝑁 𝑞 𝑞 {\displaystyle{\displaystyle Q_{n}(x)=Q_{n}\left(x;\alpha,\beta,N;q\right)={{}% _{3}\phi_{2}}\left({q^{-n},\alpha\beta q^{n+1},x\atop\alpha q,q^{-N}};q,q% \right),}}
    0 references
    DLMF id
    DLMF:18.27.E3
    0 references
    constraint
    n = 0 , 1 , … , N 𝑛 0 1 … 𝑁 {\displaystyle{\displaystyle n=0,1,\dots,N}}
    0 references
    Symbols used
    basic hypergeometric (or $$q$$ -hypergeometric) function
    test
    ϕ s r + 1 ⁡ ( a 0 , … , a r ; b 1 , … , b s ; q , z ) q-hypergeometric-rphis 𝑟 1 𝑠 subscript 𝑎 0 … subscript 𝑎 𝑟 subscript 𝑏 1 … subscript 𝑏 𝑠 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{r+1}}\phi_{\NVar{s}}}\left(\NVar{a_{0},% \dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}
    xml-id
    C17.S4.E1.m2adec
    0 references
    Q11728
    test
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C18.S1.XMD3.m1adec
    0 references
    Q11726
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1bdec
    0 references
    Q11736
    test
    N 𝑁 {\displaystyle{\displaystyle N}}
    xml-id
    C18.S1.XMD7.m1dec
    0 references
    Q11727
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1bdec
    0 references
     
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