DLMF:17.6.E18 (Q5385)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:17.6.E18
No description defined

    Statements

    ϕ 1 2 ( a q , b c ; q , z ) - ϕ 1 2 ( a , b c ; q , z ) = a z 1 - b 1 - c ϕ 1 2 ( a q , b q c q ; q , z ) , q-hypergeometric-rphis 2 1 𝑎 𝑞 𝑏 𝑐 𝑞 𝑧 q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑧 𝑎 𝑧 1 𝑏 1 𝑐 q-hypergeometric-rphis 2 1 𝑎 𝑞 𝑏 𝑞 𝑐 𝑞 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({aq,b\atop c};q,z\right)-{{}% _{2}\phi_{1}}\left({a,b\atop c};q,z\right)=az\frac{1-b}{1-c}{{}_{2}\phi_{1}}% \left({aq,bq\atop cq};q,z\right),}}
    0 references
    DLMF:17.6.E18
    0 references
    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)}}
    C17.S4.E1.m2aqdec
    0 references
    q 𝑞 {\displaystyle{\displaystyle q}}
    C17.S1.XMD10.m1qdec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C17.S1.XMD7.m1kdec
    0 references