DLMF:17.7.E3 (Q5399)

From testwiki
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:17.7.E3
No description defined

    Statements

    test
    ϕ 2 2 ⁡ ( c 2 / b 2 , b 2 c , c ⁢ q ; q 2 , q ) = 1 2 ⁢ ( b 2 , q ; q 2 ) ∞ ( c , c ⁢ q ; q 2 ) ∞ ⁢ ( ( c / b ; q ) ∞ ( b ; q ) ∞ + ( - c / b ; q ) ∞ ( - b ; q ) ∞ ) . q-hypergeometric-rphis 2 2 superscript 𝑐 2 superscript 𝑏 2 superscript 𝑏 2 𝑐 𝑐 𝑞 superscript 𝑞 2 𝑞 1 2 q-multiple-Pochhammer superscript 𝑏 2 𝑞 superscript 𝑞 2 q-multiple-Pochhammer 𝑐 𝑐 𝑞 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_{2}}\left({\ifrac{c^{2}}{b^{2}},b^{2}% \atop c,cq};q^{2},q\right)=\frac{1}{2}\frac{\left(b^{2},q;q^{2}\right)_{\infty% }}{\left(c,cq;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:17.7.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.m2aadec
    0 references
    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
    Q11713
    test
    ( a 1 , a 2 , … , a r ; q ) n q-multiple-Pochhammer subscript 𝑎 1 subscript 𝑎 2 … subscript 𝑎 𝑟 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}% \right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m6abdec
    0 references
    Q11710
    test
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1bdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q5399&oldid=31141"