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DLMF:18.27.E13 - MaRDI portal

DLMF:18.27.E13 (Q6660)

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DLMF:18.27.E13
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    Statements

    DLMF defining formula
    p n ⁢ ( x ) = p n ⁡ ( x ; a , b ; q ) = ϕ 1 2 ⁡ ( q - n , a ⁢ b ⁢ q n + 1 a ⁢ q ; q , q ⁢ x ) . subscript 𝑝 𝑛 𝑥 q-Jacobi-polynomial-p 𝑛 𝑥 𝑎 𝑏 𝑞 q-hypergeometric-rphis 2 1 superscript 𝑞 𝑛 𝑎 𝑏 superscript 𝑞 𝑛 1 𝑎 𝑞 𝑞 𝑞 𝑥 {\displaystyle{\displaystyle p_{n}(x)=p_{n}\left(x;a,b;q\right)={{}_{2}\phi_{1% }}\left({q^{-n},abq^{n+1}\atop aq};q,qx\right).}}
    0 references
    Symbols used
    basic hypergeometric (or $$q$$ -hypergeometric) function
    DLMF 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.m2abdec
    0 references
    real variable
    DLMF defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C18.S1.XMD3.m1kdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1hdec
    0 references
    polynomial of degree n
    DLMF defining formula
    p n ⁢ ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}}
    xml-id
    C18.S1.XMD9.m1ddec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1idec
    0 references

    Identifiers

     
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