DLMF:17.6.E18 (Q5385): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: basic hypergeometric (or $$q$$ -hypergeometric) function / rank
 
Normal rank
Property / Symbols used: basic hypergeometric (or $$q$$ -hypergeometric) function / qualifier
 
Defining formula:

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)}}

\qgenhyperphi{\NVar{r+1}}{\NVar{s}}@{\NVar{a_{0},\dots,a_{r}}}{\NVar{b_{1},\dots,b_{s}}}{\NVar{q}}{\NVar{z}}
Property / Symbols used: basic hypergeometric (or $$q$$ -hypergeometric) function / qualifier
 
xml-id: C17.S4.E1.m2aqdec
Property / Symbols used
 
Property / Symbols used: Q11710 / rank
 
Normal rank
Property / Symbols used: Q11710 / qualifier
 
Defining formula:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q11710 / qualifier
 
xml-id: C17.S1.XMD10.m1qdec
Property / Symbols used
 
Property / Symbols used: Q11718 / rank
 
Normal rank
Property / Symbols used: Q11718 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11718 / qualifier
 
xml-id: C17.S1.XMD7.m1kdec

Latest revision as of 14:59, 2 January 2020

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DLMF:17.6.E18
No description defined

    Statements

    Defining formula
    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 id
    DLMF:17.6.E18
    0 references
    Symbols used
    basic hypergeometric (or $$q$$ -hypergeometric) function
    Defining formula
    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.m2aqdec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1qdec
    0 references
    Q11718
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C17.S1.XMD7.m1kdec
    0 references
     
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