DLMF:17.9.E3 (Q5429)

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DLMF:17.9.E3
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    Statements

    test
    ϕ 1 2 ⁡ ( a , b c ; q , z ) = ( a ⁢ b ⁢ z / c ; q ) ∞ ( b ⁢ z / c ; q ) ∞ ⁢ ϕ 2 3 ⁡ ( a , c / b , 0 c , c ⁢ q / ( b ⁢ z ) ; q , q ) + ( a , b ⁢ z , c / b ; q ) ∞ ( c , z , c / ( b ⁢ z ) ; q ) ∞ ⁢ ϕ 2 3 ⁡ ( z , a ⁢ b ⁢ z / c , 0 b ⁢ z , b ⁢ z ⁢ q / c ; q , q ) , q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑧 q-Pochhammer-symbol 𝑎 𝑏 𝑧 𝑐 𝑞 q-Pochhammer-symbol 𝑏 𝑧 𝑐 𝑞 q-hypergeometric-rphis 3 2 𝑎 𝑐 𝑏 0 𝑐 𝑐 𝑞 𝑏 𝑧 𝑞 𝑞 q-multiple-Pochhammer 𝑎 𝑏 𝑧 𝑐 𝑏 𝑞 q-multiple-Pochhammer 𝑐 𝑧 𝑐 𝑏 𝑧 𝑞 q-hypergeometric-rphis 3 2 𝑧 𝑎 𝑏 𝑧 𝑐 0 𝑏 𝑧 𝑏 𝑧 𝑞 𝑐 𝑞 𝑞 {\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({a,b\atop c};q,z\right)=% \frac{\left(abz/c;q\right)_{\infty}}{\left(bz/c;q\right)_{\infty}}{{}_{3}\phi_% {2}}\left({a,c/b,0\atop c,cq/(bz)};q,q\right)+\frac{\left(a,bz,c/b;q\right)_{% \infty}}{\left(c,z,c/(bz);q\right)_{\infty}}{{}_{3}\phi_{2}}\left({z,abz/c,0% \atop bz,bzq/c};q,q\right),}}
    0 references
    DLMF id
    DLMF:17.9.E3
    0 references
    Symbols used
    Q11298
    test
    ( 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.m2abdec
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    basic hypergeometric (or $$q$$ -hypergeometric) function
    test
    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
     
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