DLMF:18.27.E5 (Q5956): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1cdec

Latest revision as of 01:48, 2 January 2020

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DLMF:18.27.E5
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    Statements

    Defining formula
    P n ⁡ ( x ; a , b , c ; q ) = ϕ 2 3 ⁡ ( q - n , a ⁢ b ⁢ q n + 1 , x a ⁢ q , c ⁢ q ; q , q ) , q-Jacobi-polynomial-P 𝑛 𝑥 𝑎 𝑏 𝑐 𝑞 q-hypergeometric-rphis 3 2 superscript 𝑞 𝑛 𝑎 𝑏 superscript 𝑞 𝑛 1 𝑥 𝑎 𝑞 𝑐 𝑞 𝑞 𝑞 {\displaystyle{\displaystyle P_{n}\left(x;a,b,c;q\right)={{}_{3}\phi_{2}}\left% ({q^{-n},abq^{n+1},x\atop aq,cq};q,q\right),}}
    0 references
    DLMF id
    DLMF:18.27.E5
    0 references
    Symbols used
    basic hypergeometric (or $$q$$ -hypergeometric) function
    Defining formula
    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.m2aadec
    0 references
    Q11728
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C18.S1.XMD3.m1cdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1ddec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1cdec
    0 references
     
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