DLMF:17.10.E5 (Q5451): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11721 / rank
 
Normal rank
Property / Symbols used: Q11721 / qualifier
 
Defining formula:

idem ⁡ ( χ 1 ; χ 2 , … , χ n ) idem subscript 𝜒 1 subscript 𝜒 2 … subscript 𝜒 𝑛 {\displaystyle{\displaystyle\mathrm{idem}\left(\NVar{\chi_{1}};\NVar{\chi_{2},% \dots,\chi_{n}}\right)}}

\idem@{\NVar{\chi_{1}}}{\NVar{\chi_{2},\dots,\chi_{n}}}
Property / Symbols used: Q11721 / qualifier
 
xml-id: C17.S1.p3.m2adec

Revision as of 15:08, 2 January 2020

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DLMF:17.10.E5
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    Statements

    Defining formula
    ( a ⁢ q / b , a ⁢ q / c , a ⁢ q / d , a ⁢ q / e , q / ( a ⁢ b ) , q / ( a ⁢ c ) , q / ( a ⁢ d ) , q / ( a ⁢ e ) ; q ) ∞ ( f ⁢ a , g ⁢ a , f / a , g / a , q ⁢ a 2 , q / a 2 ; q ) ∞ ⁢ ψ 8 8 ⁡ ( q ⁢ a , - q ⁢ a , b ⁢ a , c ⁢ a , d ⁢ a , e ⁢ a , f ⁢ a , g ⁢ a a , - a , a ⁢ q / b , a ⁢ q / c , a ⁢ q / d , a ⁢ q / e , a ⁢ q / f , a ⁢ q / g ; q , q 2 b ⁢ c ⁢ d ⁢ e ⁢ f ⁢ g ) = ( q , q / ( b ⁢ f ) , q / ( c ⁢ f ) , q / ( d ⁢ f ) , q / ( e ⁢ f ) , q ⁢ f / b , q ⁢ f / c , q ⁢ f / d , q ⁢ f / e ; q ) ∞ ( f ⁢ a , q / ( f ⁢ a ) , a ⁢ q / f , f / a , g / f , f ⁢ g , q ⁢ f 2 ; q ) ∞ ⁢ ϕ 7 8 ⁡ ( f 2 , q ⁢ f , - q ⁢ f , f ⁢ b , f ⁢ c , f ⁢ d , f ⁢ e , f ⁢ g f , - f , f ⁢ q / b , f ⁢ q / c , f ⁢ q / d , f ⁢ q / e , f ⁢ q / g ; q , q 2 b ⁢ c ⁢ d ⁢ e ⁢ f ⁢ g ) + idem ⁡ ( f ; g ) . q-multiple-Pochhammer 𝑎 𝑞 𝑏 𝑎 𝑞 𝑐 𝑎 𝑞 𝑑 𝑎 𝑞 𝑒 𝑞 𝑎 𝑏 𝑞 𝑎 𝑐 𝑞 𝑎 𝑑 𝑞 𝑎 𝑒 𝑞 q-multiple-Pochhammer 𝑓 𝑎 𝑔 𝑎 𝑓 𝑎 𝑔 𝑎 𝑞 superscript 𝑎 2 𝑞 superscript 𝑎 2 𝑞 q-hypergeometric-rpsis 8 8 𝑞 𝑎 𝑞 𝑎 𝑏 𝑎 𝑐 𝑎 𝑑 𝑎 𝑒 𝑎 𝑓 𝑎 𝑔 𝑎 𝑎 𝑎 𝑎 𝑞 𝑏 𝑎 𝑞 𝑐 𝑎 𝑞 𝑑 𝑎 𝑞 𝑒 𝑎 𝑞 𝑓 𝑎 𝑞 𝑔 𝑞 superscript 𝑞 2 𝑏 𝑐 𝑑 𝑒 𝑓 𝑔 q-multiple-Pochhammer 𝑞 𝑞 𝑏 𝑓 𝑞 𝑐 𝑓 𝑞 𝑑 𝑓 𝑞 𝑒 𝑓 𝑞 𝑓 𝑏 𝑞 𝑓 𝑐 𝑞 𝑓 𝑑 𝑞 𝑓 𝑒 𝑞 q-multiple-Pochhammer 𝑓 𝑎 𝑞 𝑓 𝑎 𝑎 𝑞 𝑓 𝑓 𝑎 𝑔 𝑓 𝑓 𝑔 𝑞 superscript 𝑓 2 𝑞 q-hypergeometric-rphis 8 7 superscript 𝑓 2 𝑞 𝑓 𝑞 𝑓 𝑓 𝑏 𝑓 𝑐 𝑓 𝑑 𝑓 𝑒 𝑓 𝑔 𝑓 𝑓 𝑓 𝑞 𝑏 𝑓 𝑞 𝑐 𝑓 𝑞 𝑑 𝑓 𝑞 𝑒 𝑓 𝑞 𝑔 𝑞 superscript 𝑞 2 𝑏 𝑐 𝑑 𝑒 𝑓 𝑔 idem 𝑓 𝑔 {\displaystyle{\displaystyle\frac{\left(aq/b,aq/c,aq/d,aq/e,q/(ab),q/(ac),q/(% ad),q/(ae);q\right)_{\infty}}{\left(fa,ga,f/a,g/a,qa^{2},q/a^{2};q\right)_{% \infty}}\*{{}_{8}\psi_{8}}\left({qa,-qa,ba,ca,da,ea,fa,ga\atop a,-a,aq/b,aq/c,% aq/d,aq/e,aq/f,aq/g};q,\frac{q^{2}}{bcdefg}\right)=\frac{\left(q,q/(bf),q/(cf)% ,q/(df),q/(ef),qf/b,qf/c,qf/d,qf/e;q\right)_{\infty}}{\left(fa,q/(fa),aq/f,f/a% ,g/f,fg,qf^{2};q\right)_{\infty}}\*{{}_{8}\phi_{7}}\left({f^{2},qf,-qf,fb,fc,% fd,fe,fg\atop f,-f,fq/b,fq/c,fq/d,fq/e,fq/g};q,\frac{q^{2}}{bcdefg}\right)+% \mathrm{idem}\left(f;g\right).}}
    0 references
    DLMF id
    DLMF:17.10.E5
    0 references
    Symbols used
    Q11721
    Defining formula
    idem ⁡ ( χ 1 ; χ 2 , … , χ n ) idem subscript 𝜒 1 subscript 𝜒 2 … subscript 𝜒 𝑛 {\displaystyle{\displaystyle\mathrm{idem}\left(\NVar{\chi_{1}};\NVar{\chi_{2},% \dots,\chi_{n}}\right)}}
    xml-id
    C17.S1.p3.m2adec
    0 references
     
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