DLMF:17.10.E6 (Q5452): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:17.10.E6	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\frac{\left(aq/b,aq/c,aq/d,aq/e,aq/f,q/(ab),q/(ac)% ,q/(ad),q/(ae),q/(af);q\right)_{\infty}}{\left(ag,ah,ak,g/a,h/a,k/a,qa^{2},q/a% ^{2};q\right)_{\infty}}\*{{}_{10}\psi_{10}}\left({qa,-qa,ba,ca,da,ea,fa,ga,ha,% ka\atop a,-a,aq/b,aq/c,aq/d,aq/e,aq/f,aq/g,aq/h,aq/k};q,\frac{q^{2}}{bcdefghk}% \right)=\frac{\left(q,q/(bg),q/(cg),q/(dg),q/(eg),q/(fg),qg/b,qg/c,qg/d,qg/e,% qg/f;q\right)_{\infty}}{\left(gh,gk,h/g,ag,q/(ag),g/a,aq/g,qg^{2};q\right)_{% \infty}}\*{{}_{10}\phi_{9}}\left({g^{2},qg,-qg,gb,gc,gd,ge,gf,gh,gk\atop g,-g,% qg/b,qg/c,qg/d,qg/e,qg/f,qg/h,qg/k};q,\frac{q^{2}}{bcdefghk}\right)+\mathrm{% idem}\left(g;h,k\right).}}

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DLMF:17.10.E6

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Defining formula

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

C17.S1.p3.m2aadec

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basic hypergeometric (or $$q$$ -hypergeometric) function

Defining formula

{\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)}}

C17.S4.E1.m2aadec

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bilateral basic hypergeometric (or bilateral $$q$$ -hypergeometric) function

Defining formula

{\displaystyle{\displaystyle{{}_{\NVar{r}}\psi_{\NVar{s}}}\left(\NVar{a_{1},% \dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}

C17.S4.E3.m2aedec

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Defining formula

{\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}% \right)_{\NVar{n}}}}

C17.S2.SS1.p1.m6aedec

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