# Correction: Cohl, H.S.; Costas-Santos, R.S.; Ge, L. Terminating Basic Hypergeometric Representations and Transformations for the Askey–Wilson Polynomials Symmetry 2020, 12, 1290

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- In the line immediately following (15), replace $qabc=def$ with ${q}^{1-n}abc=def$.
- Replace the two Equations (35) and (36) with the following four equations, which should then be listed as (35)–(38), respectively (note that this will push all the equation numbers originally starting from (37) to whatever their equation numbers used to be plus an additional two):$$=\frac{{\left(\frac{qb}{de},\frac{qb}{df},\frac{qb}{ef},qb;q\right)}_{n}}{{\left(\frac{qb}{def},\frac{qb}{d},\frac{qb}{e},\frac{qb}{f};q\right)}_{n}}{}_{8}{W}_{7}\left(\frac{{q}^{-n-1}def}{b};{q}^{-n},d,e,f,\frac{{q}^{-n-1}cdef}{{b}^{2}};q,\frac{q}{c}\right)$$$$=\frac{{\left(\frac{{q}^{2}{b}^{2}}{cdef},qb,d,e,f;q\right)}_{n}}{{\left(\frac{def}{qb},\frac{qb}{c},\frac{qb}{d},\frac{qb}{e},\frac{qb}{f};q\right)}_{n}}{}_{8}{W}_{7}\left(\frac{{q}^{1-n}b}{def};{q}^{-n},\frac{{q}^{-n}c}{b},\frac{qb}{de},\frac{qb}{df},\frac{qb}{ef};q,\frac{q}{c}\right)$$$$=\frac{{\left(\frac{{q}^{2}{b}^{2}}{cdef},qb;q\right)}_{n}}{{\left(\frac{qb}{c},\frac{{q}^{2}{b}^{2}}{def};q\right)}_{n}}{}_{8}{W}_{7}\left(\frac{q{b}^{2}}{def};{q}^{-n},\frac{qb}{de},\frac{qb}{df},\frac{qb}{ef},c;q,\frac{{q}^{n+1}b}{c}\right)$$$$\begin{array}{l}={q}^{\left(\begin{array}{c}n\\ 2\end{array}\right)}{\left(-\frac{qb}{c}\right)}^{n}\frac{{\left(\frac{q{b}^{2}}{def},\frac{qb}{ef},\frac{qb}{de},\frac{qb}{df},qb,c;q\right)}_{n}}{{\left(\frac{q{b}^{2}}{def};q\right)}_{2n}{\left(\frac{qb}{c},\frac{qb}{d},\frac{qb}{e},\frac{qb}{f};q\right)}_{n}}\\ \times {}_{8}{W}_{7}\left(\frac{{q}^{-2n-1}def}{{b}^{2}};{q}^{-n},\frac{{q}^{-n}d}{b},\frac{{q}^{-n}e}{b},\frac{{q}^{-n}f}{b},\frac{{q}^{-n-1}cdef}{{b}^{2}};q,\frac{{q}^{n+1}b}{c}\right)\end{array}$$
- In the proof of Corollary 3, replace “. Then,” with “, setting $\theta $↦$-\theta $ where necessary. Then,”.
- Replace (44) and (45), respectively (with the updated numbers these will become (46) and (47)) with:$$=\frac{{\left(\frac{qb}{ed},\frac{qb}{ef},\frac{qb}{c},\frac{d}{c},c;q\right)}_{n}}{{\left(\frac{qb}{ce},\frac{qb}{cf},\frac{qb}{d},\frac{c}{e},d;q\right)}_{n}}{}_{8}{W}_{7}\left(\frac{{q}^{-n}e}{c};{q}^{-n},\frac{{q}^{-n}e}{b},\frac{qb}{cd},\frac{qb}{cf},e;q,\frac{df}{b}\right)$$$$=\frac{{\left(\frac{qb}{cd},\frac{qb}{f},\frac{d}{c},f;q\right)}_{n}}{{\left(\frac{qb}{cf},\frac{qb}{d},\frac{f}{c},d;q\right)}_{n}}{}_{8}{W}_{7}\left(\frac{{q}^{-n}c}{f};{q}^{-n},\frac{{q}^{-n}c}{b},\frac{qb}{ef},\frac{qb}{df},c;q,\frac{de}{b}\right)$$
- Replace the text in Remark 5 (note that we refer to the updated equation numbers) as: “Other sets of parameter interchange transformations can be obtained by considering all permutations of the symmetric parameters c,d,e,f in (35), (36), (38), respectively. However, one can see that these are equivalent to the above Corollary 5 by replacing:$$\left(b,c,d,e,f\right)\mapsto \left(\frac{{q}^{-2n-1}def}{{b}^{2}},\frac{{q}^{-n-1}cdef}{{b}^{2}},\frac{{q}^{-n}f}{b},\frac{{q}^{-n}e}{b},\frac{{q}^{-n}d}{b}\right),$$$$\left(b,c,d,e,f\right)\mapsto \left(\frac{{q}^{-2n-1}cde}{{b}^{2}},\frac{{q}^{-n-1}cdef}{{b}^{2}},\frac{{q}^{-n}c}{b},\frac{{q}^{-n}d}{b},\frac{{q}^{-n}e}{b}\right),$$$$\left(b,c,d,e,f\right)\mapsto \left(\frac{{q}^{-n-1}def}{b},\frac{{q}^{-n-1}cdef}{{b}^{2}},f,e,d\right),$$
- Replace “
**Funding:**This research received no external funding.” with “**Funding:**R.S.C.-S. acknowledges financial support through the research project PGC2018-09504-B-C33 supported by Agencia Estatal de Investigaci$\stackrel{\xb4}{\mathrm{o}}$n of Spain.”. - In the line before “
**Conflicts of Interest:**…”, insert “**Acknowledgments:**H.S.C. would like to thank Mourad Ismail for valuable discussions.”.

## Reference

- Cohl, H.S.; Costas-Santos, R.S.; Ge, L. Terminating Basic Hypergeometric Representations and Transformations for the Askey-Wilson Polynomials. Symmetry
**2020**, 12, 1290. [Google Scholar] [CrossRef]

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**MDPI and ACS Style**

Cohl, H.S.; Costas-Santos, R.S.; Ge, L.
Correction: Cohl, H.S.; Costas-Santos, R.S.; Ge, L. Terminating Basic Hypergeometric Representations and Transformations for the Askey–Wilson Polynomials *Symmetry* 2020, *12*, 1290. *Symmetry* **2020**, *12*, 2120.
https://doi.org/10.3390/sym12122120

**AMA Style**

Cohl HS, Costas-Santos RS, Ge L.
Correction: Cohl, H.S.; Costas-Santos, R.S.; Ge, L. Terminating Basic Hypergeometric Representations and Transformations for the Askey–Wilson Polynomials *Symmetry* 2020, *12*, 1290. *Symmetry*. 2020; 12(12):2120.
https://doi.org/10.3390/sym12122120

**Chicago/Turabian Style**

Cohl, Howard S., Roberto S. Costas-Santos, and Linus Ge.
2020. "Correction: Cohl, H.S.; Costas-Santos, R.S.; Ge, L. Terminating Basic Hypergeometric Representations and Transformations for the Askey–Wilson Polynomials *Symmetry* 2020, *12*, 1290" *Symmetry* 12, no. 12: 2120.
https://doi.org/10.3390/sym12122120