Definition:qHyperrWs

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The LaTeX DLMF and DRMF macro \qHyperrWs represents the ${\displaystyle{\displaystyle q}}$-hypergeometric series.

This macro is in the category of real or complex valued functions.

In math mode, this macro can be called in the following ways:

\qHyperrWs{r}{r+1} produces ${\displaystyle{\displaystyle{\displaystyle{{}_{r}W_{r+1}}}}}$

\qHyperrWs{r}{r+1}@{a_1}{a_4,a_5,...,a_{r+1}}{q}{z} produces ${\displaystyle{\displaystyle{\displaystyle{{}_{r}W_{r+1}}\!\left(a_{1};a_{4},a_{5},...,a_{r+1};q,z\right)}}}$

\qHyperrWs{r}{r+1}@@{a_1}{a_4,a_5,...,a_{r+1}}{q}{z} produces ${\displaystyle{\displaystyle{\displaystyle{{}_{r}W_{r+1}}\!\left({a_{1}\atop a_{4},a_{5},...,a_{r+1}};q,z\right)}}}$

\qHyperrWs{r}{r+1}@@@{a_1}{a_4,a_5,...,a_{r+1}}{q}{z} produces ${\displaystyle{\displaystyle{\displaystyle{{}_{r}W_{r+1}}\!\left(q,z\right)}}}$

These are defined by ${\displaystyle{\displaystyle{{}_{r+1}W_{r}}\!\left(a_{1};a_{4},a_{5},\ldots,a_{r+1};q,z\right):=\qHyperrphis{r+1}r@@{a_{1},qa_{1}^{\frac{1}{2}},-qa_{1}^{\frac{1}{2}},a_{4},\ldots,a_{r+1}}{a_{1}^{\frac{1}{2}},-a_{1}^{\frac{1}{2}},qa_{1}/a_{4},\ldots,qa_{1}/a_{r+1}}qz.}}$

Bibliography

Equation (2.1.11) of GaR.

Symbols List

${\displaystyle{\displaystyle{\displaystyle{{}_{r+1}W_{r}}}}}$ : very-well-poised basic hypergeometric (or ${\displaystyle{\displaystyle{\displaystyle q}}}$-hypergeometric) function : http://drmf.wmflabs.org/wiki/Definition:qHyperrWs
${\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}$ : basic hypergeometric (or ${\displaystyle{\displaystyle{\displaystyle q}}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1

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