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DLMF:18.28.E5 - MaRDI portal

DLMF:18.28.E5 (Q6676)

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DLMF:18.28.E5
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    Statements

    DLMF defining formula
    h n = h 0 ⁢ ( 1 - a ⁢ b ⁢ c ⁢ d ⁢ q n - 1 ) ⁢ ( q , a ⁢ b , a ⁢ c , a ⁢ d , b ⁢ c , b ⁢ d , c ⁢ d ; q ) n ( 1 - a ⁢ b ⁢ c ⁢ d ⁢ q 2 ⁢ n - 1 ) ⁢ ( a ⁢ b ⁢ c ⁢ d ; q ) n , subscript ℎ 𝑛 subscript ℎ 0 1 𝑎 𝑏 𝑐 𝑑 superscript 𝑞 𝑛 1 q-multiple-Pochhammer 𝑞 𝑎 𝑏 𝑎 𝑐 𝑎 𝑑 𝑏 𝑐 𝑏 𝑑 𝑐 𝑑 𝑞 𝑛 1 𝑎 𝑏 𝑐 𝑑 superscript 𝑞 2 𝑛 1 q-Pochhammer-symbol 𝑎 𝑏 𝑐 𝑑 𝑞 𝑛 {\displaystyle{\displaystyle h_{n}=h_{0}\frac{(1-abcdq^{n-1})\left(q,ab,ac,ad,% bc,bd,cd;q\right)_{n}}{(1-abcdq^{2n-1})\left(abcd;q\right)_{n}},}}
    0 references
    constraint
    n = 1 , 2 , … 𝑛 1 2 … {\displaystyle{\displaystyle n=1,2,\ldots}}
    0 references
    Symbols used
    Q11269
    DLMF defining formula
    ( a ; q ) n q-Pochhammer-symbol 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m2acdec
    0 references
    Q11684
    DLMF defining formula
    ( a 1 , a 2 , … , a r ; q ) n q-multiple-Pochhammer subscript 𝑎 1 subscript 𝑎 2 … subscript 𝑎 𝑟 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}% \right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m6acdec
    0 references
    real variable
    DLMF defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C18.S1.XMD3.m1cdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1bdec
    0 references
    18.2.E5
    DLMF defining formula
    h n subscript ℎ 𝑛 {\displaystyle{\displaystyle h_{n}}}
    xml-id
    C18.S2.XMD4.m1bdec
    0 references

    Identifiers

     
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