DLMF:17.6.E27 (Q5394): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11710 / rank
 
Normal rank
Property / Symbols used: Q11710 / qualifier
 
test:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q11710 / qualifier
 
xml-id: C17.S1.XMD10.m1zdec

Revision as of 14:00, 2 January 2020

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DLMF:17.6.E27
No description defined

    Statements

    test
    z ⁢ ( c - a ⁢ b ⁢ q ⁢ z ) ⁢ 𝒟 q 2 ⁢ ϕ 1 2 ⁡ ( a , b c ; q , z ) + ( 1 - c 1 - q + ( 1 - a ) ⁢ ( 1 - b ) - ( 1 - a ⁢ b ⁢ q ) 1 - q ⁢ z ) ⁢ 𝒟 q ⁢ ϕ 1 2 ⁡ ( a , b c ; q , z ) - ( 1 - a ) ⁢ ( 1 - b ) ( 1 - q ) 2 ⁢ ϕ 1 2 ⁡ ( a , b c ; q , z ) = 0 . 𝑧 𝑐 𝑎 𝑏 𝑞 𝑧 superscript subscript 𝒟 𝑞 2 q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑧 1 𝑐 1 𝑞 1 𝑎 1 𝑏 1 𝑎 𝑏 𝑞 1 𝑞 𝑧 subscript 𝒟 𝑞 q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑧 1 𝑎 1 𝑏 superscript 1 𝑞 2 q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑧 0 {\displaystyle{\displaystyle z(c-abqz)\mathcal{D}_{q}^{2}{{}_{2}\phi_{1}}\left% ({a,b\atop c};q,z\right)+\left(\frac{1-c}{1-q}+\frac{(1-a)(1-b)-(1-abq)}{1-q}z% \right)\mathcal{D}_{q}{{}_{2}\phi_{1}}\left({a,b\atop c};q,z\right)-\frac{(1-a% )(1-b)}{(1-q)^{2}}{{}_{2}\phi_{1}}\left({a,b\atop c};q,z\right)=0.}}
    0 references
    DLMF id
    DLMF:17.6.E27
    0 references
    Symbols used
    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.m2azdec
    0 references
    Q11710
    test
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1zdec
    0 references
     
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