DLMF:17.2.E22 (Q5312)

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DLMF:17.2.E22
No description defined

    Statements

    Defining formula
    ( q ⁢ a 1 2 , - q ⁢ a 1 2 ; q ) n ( a 1 2 , - a 1 2 ; q ) n = ( a ⁢ q 2 ; q 2 ) n ( a ; q 2 ) n = 1 - a ⁢ q 2 ⁢ n 1 - a , q-multiple-Pochhammer 𝑞 superscript 𝑎 1 2 𝑞 superscript 𝑎 1 2 𝑞 𝑛 q-multiple-Pochhammer superscript 𝑎 1 2 superscript 𝑎 1 2 𝑞 𝑛 q-Pochhammer-symbol 𝑎 superscript 𝑞 2 superscript 𝑞 2 𝑛 q-Pochhammer-symbol 𝑎 superscript 𝑞 2 𝑛 1 𝑎 superscript 𝑞 2 𝑛 1 𝑎 {\displaystyle{\displaystyle\frac{\left(qa^{\frac{1}{2}},-qa^{\frac{1}{2}};q% \right)_{n}}{\left(a^{\frac{1}{2}},-a^{\frac{1}{2}};q\right)_{n}}=\frac{\left(% aq^{2};q^{2}\right)_{n}}{\left(a;q^{2}\right)_{n}}=\frac{1-aq^{2n}}{1-a},}}
    0 references
    DLMF id
    DLMF:17.2.E22
    0 references
    Symbols used
    Q11298
    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.m2audec
    0 references
    Q11713
    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.m6addec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1udec
    0 references
     
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