Next Article in Journal
Real-Time Data Filling and Automatic Retrieval Algorithm of Road Traffic Based on Deep-Learning Method
Previous Article in Journal
ICONet: A Lightweight Network with Greater Environmental Adaptivity
Previous Article in Special Issue
Multi-Integral Representations for Associated Legendre and Ferrers Functions
 
 
Due to planned maintenance work on our platforms, there might be short service disruptions on Saturday, December 3rd, between 15:00 and 16:00 (CET).
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Correction

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

1
Applied and Computational Mathematics Division, National Institute of Standards and Technology, Mission Viejo, CA 92694, USA
2
Departamento de Física y Matemáticas, Universidad de Alcalá, 28871 Alcalá de Henares, Spain
3
Department of Mathematics, University of Rochester, Rochester, NY 14627, USA
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(12), 2120; https://doi.org/10.3390/sym12122120
Received: 18 November 2020 / Accepted: 24 November 2020 / Published: 21 December 2020
(This article belongs to the Special Issue Symmetry in Special Functions and Orthogonal Polynomials)
The authors wish to make the following corrections to their paper [1]:
  • In the line immediately following (15), replace q a b c = d e f with q 1 n a b c = d e f .
  • 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):
    = ( q b d e , q b d f , q b e f , q b ; q ) n ( q b d e f , q b d , q b e , q b f ; q ) n 8 W 7 ( q n 1 d e f b ; q n , d , e , f , q n 1 c d e f b 2 ; q , q c )
    = ( q 2 b 2 c d e f , q b , d , e , f ; q ) n ( d e f q b , q b c , q b d , q b e , q b f ; q ) n 8 W 7 ( q 1 n b d e f ; q n , q n c b , q b d e , q b d f , q b e f ; q , q c )
    = ( q 2 b 2 c d e f , q b ; q ) n ( q b c , q 2 b 2 d e f ; q ) n 8 W 7 ( q b 2 d e f ; q n , q b d e , q b d f , q b e f , c ; q , q n + 1 b c )
    = q ( n 2 ) ( q b c ) n ( q b 2 d e f , q b e f , q b d e , q b d f , q b , c ; q ) n ( q b 2 d e f ; q ) 2 n ( q b c , q b d , q b e , q b f ; q ) n × 8 W 7 ( q 2 n 1 d e f b 2 ; q n , q n d b , q n e b , q n f b , q n 1 c d e f b 2 ; q , q n + 1 b c )
  • In the proof of Corollary 3, replace “. Then,” with “, setting θ θ where necessary. Then,”.
  • Replace (44) and (45), respectively (with the updated numbers these will become (46) and (47)) with:
    = ( q b e d , q b e f , q b c , d c , c ; q ) n ( q b c e , q b c f , q b d , c e , d ; q ) n 8 W 7 ( q n e c ; q n , q n e b , q b c d , q b c f , e ; q , d f b )
    = ( q b c d , q b f , d c , f ; q ) n ( q b c f , q b d , f c , d ; q ) n 8 W 7 ( q n c f ; q n , q n c b , q b e f , q b d f , c ; q , d e b )
  • 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:
    ( b , c , d , e , f ) ( q 2 n 1 d e f b 2 , q n 1 c d e f b 2 , q n f b , q n e b , q n d b ) ,
    ( b , c , d , e , f ) ( q 2 n 1 c d e b 2 , q n 1 c d e f b 2 , q n c b , q n d b , q n e b ) ,
    ( b , c , d , e , f ) ( q n 1 d e f b , q n 1 c d e f b 2 , f , e , d ) ,
    respectively”.
  • 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 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.”.
The authors would like to apologize for any inconvenience caused to the readers by these changes. The changes do not affect the scientific results. The manuscript will be updated, and the original will remain online on the article webpage, with a reference to this correction.

Reference

  1. 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]
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Share and Cite

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

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop