DLMF:17.6.E4 (Q5371): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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.m2acdec

Revision as of 14:57, 2 January 2020

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DLMF:17.6.E4
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    Statements

    Defining formula
    ϕ 1 2 ⁡ ( b 2 , b 2 / c c ; q 2 , c ⁢ q / b 2 ) = 1 2 ⁢ ( b 2 , q ; q 2 ) ∞ ( c , c ⁢ q / b 2 ; q 2 ) ∞ ⁢ ( ( c / b ; q ) ∞ ( b ; q ) ∞ + ( - c / b ; q ) ∞ ( - b ; q ) ∞ ) , q-hypergeometric-rphis 2 1 superscript 𝑏 2 superscript 𝑏 2 𝑐 𝑐 superscript 𝑞 2 𝑐 𝑞 superscript 𝑏 2 1 2 q-multiple-Pochhammer superscript 𝑏 2 𝑞 superscript 𝑞 2 q-multiple-Pochhammer 𝑐 𝑐 𝑞 superscript 𝑏 2 superscript 𝑞 2 q-Pochhammer-symbol 𝑐 𝑏 𝑞 q-Pochhammer-symbol 𝑏 𝑞 q-Pochhammer-symbol 𝑐 𝑏 𝑞 q-Pochhammer-symbol 𝑏 𝑞 {\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({b^{2},\ifrac{b^{2}}{c}\atop c% };q^{2},\ifrac{cq}{b^{2}}\right)=\frac{1}{2}\frac{\left(b^{2},q;q^{2}\right)_{% \infty}}{\left(c,cq/b^{2};q^{2}\right)_{\infty}}\left(\frac{\left(c/b;q\right)% _{\infty}}{\left(b;q\right)_{\infty}}+\frac{\left(-c/b;q\right)_{\infty}}{% \left(-b;q\right)_{\infty}}\right),}}
    0 references
    DLMF id
    DLMF:17.6.E4
    0 references
    constraint
    | c ⁢ q | < | b 2 | 𝑐 𝑞 superscript 𝑏 2 {\displaystyle{\displaystyle|cq|<|b^{2}|}}
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    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.m2abdec
    0 references
    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.m2acdec
    0 references
     
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