DLMF:17.10.E5 (Q5451)

From DRMF

Jump to navigation Jump to search

No description defined

Language	Label	Description	Also known as
English	DLMF:17.10.E5	No description defined

Statements

Defining formula

{\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:17.10.E5

0 references

Defining formula

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

C17.S1.p3.m2adec

0 references

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.m2adec

0 references

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.m2addec

0 references

Defining formula

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

C17.S2.SS1.p1.m6addec

0 references

Defining formula

{\displaystyle{\displaystyle q}}

C17.S1.XMD10.m1ddec

0 references

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5451&oldid=54735"