DLMF:18.27.E4 (Q5955)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:18.27.E4
No description defined

    Statements

    Defining formula
    ∑ y = 0 N Q n ⁢ ( q - y ) ⁢ Q m ⁢ ( q - y ) ⁢ ( α ⁢ q , q - N ; q ) y ⁢ ( α ⁢ β ⁢ q ) - y ( q , β - 1 ⁢ q - N ; q ) y = h n ⁢ δ n , m , superscript subscript 𝑦 0 𝑁 subscript 𝑄 𝑛 superscript 𝑞 𝑦 subscript 𝑄 𝑚 superscript 𝑞 𝑦 subscript 𝛼 𝑞 superscript 𝑞 𝑁 𝑞 𝑦 superscript 𝛼 𝛽 𝑞 𝑦 subscript 𝑞 superscript 𝛽 1 superscript 𝑞 𝑁 𝑞 𝑦 subscript ℎ 𝑛 Kronecker 𝑛 𝑚 {\displaystyle{\displaystyle\sum_{y=0}^{N}Q_{n}(q^{-y})Q_{m}(q^{-y})\frac{(% \alpha q,q^{-N};q)_{y}(\alpha\beta q)^{-y}}{(q,\beta^{-1}q^{-N};q)_{y}}=h_{n}% \delta_{n,m},}}
    0 references
    DLMF id
    DLMF:18.27.E4
    0 references
    constraint
    n , m = 0 , 1 , … , N formulae-sequence 𝑛 𝑚 0 1 … 𝑁 {\displaystyle{\displaystyle n,m=0,1,\ldots,N}}
    0 references
    Symbols used
    Q10768
    Defining formula
    δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}
    xml-id
    introduction.Sx4.p1.t1.r4.m5aadec
    0 references
    Q11743
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C18.S1.XMD1.m1dec
    0 references
    Q11728
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C18.S1.XMD3.m1bdec
    0 references
    Q11730
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C18.S1.XMD5.m1adec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1cdec
    0 references
    Q11736
    Defining formula
    N 𝑁 {\displaystyle{\displaystyle N}}
    xml-id
    C18.S1.XMD7.m1adec
    0 references
    DLMF:18.2.E5
    Defining formula
    h n subscript ℎ 𝑛 {\displaystyle{\displaystyle h_{n}}}
    xml-id
    C18.S2.XMD4.m1adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5955&oldid=34722"