The Cauchy operator plays important roles in the theory of basic hypergeometric series. As some applications, our purpose is mainly to show new proofs of the Mehler’s formula, the Rogers formula and the generating function for the homogeneous Hahn polynomials Φ(α)n(x,y|q)) by making use of the Cauchy operator and its properties. In addition, some interesting results are also obtained, which include a formal extension of the generating function for Φ(α)n(x,y|q)).
| Published in | American Journal of Applied Mathematics (Volume 9, Issue 3) |
| DOI | 10.11648/j.ajam.20210903.11 |
| Page(s) | 64-69 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
The Cauchy Operator, The Hahn Polynomials, Mehler’s Formula, Rogers Formula
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APA Style
Qiuxia Hu, Xinhao Huang, Zhizheng Zhang. (2021). The Cauchy Operator and the Homogeneous Hahn Polynomials. American Journal of Applied Mathematics, 9(3), 64-69. https://doi.org/10.11648/j.ajam.20210903.11
ACS Style
Qiuxia Hu; Xinhao Huang; Zhizheng Zhang. The Cauchy Operator and the Homogeneous Hahn Polynomials. Am. J. Appl. Math. 2021, 9(3), 64-69. doi: 10.11648/j.ajam.20210903.11
AMA Style
Qiuxia Hu, Xinhao Huang, Zhizheng Zhang. The Cauchy Operator and the Homogeneous Hahn Polynomials. Am J Appl Math. 2021;9(3):64-69. doi: 10.11648/j.ajam.20210903.11
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Download@article{10.11648/j.ajam.20210903.11,
author = {Qiuxia Hu and Xinhao Huang and Zhizheng Zhang},
title = {The Cauchy Operator and the Homogeneous Hahn Polynomials},
journal = {American Journal of Applied Mathematics},
volume = {9},
number = {3},
pages = {64-69},
doi = {10.11648/j.ajam.20210903.11},
url = {https://doi.org/10.11648/j.ajam.20210903.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20210903.11},
abstract = {The Cauchy operator plays important roles in the theory of basic hypergeometric series. As some applications, our purpose is mainly to show new proofs of the Mehler’s formula, the Rogers formula and the generating function for the homogeneous Hahn polynomials Φ(α)n(x,y|q)) by making use of the Cauchy operator and its properties. In addition, some interesting results are also obtained, which include a formal extension of the generating function for Φ(α)n(x,y|q)).},
year = {2021}
}
TY - JOUR T1 - The Cauchy Operator and the Homogeneous Hahn Polynomials AU - Qiuxia Hu AU - Xinhao Huang AU - Zhizheng Zhang Y1 - 2021/05/27 PY - 2021 N1 - https://doi.org/10.11648/j.ajam.20210903.11 DO - 10.11648/j.ajam.20210903.11 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 64 EP - 69 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20210903.11 AB - The Cauchy operator plays important roles in the theory of basic hypergeometric series. As some applications, our purpose is mainly to show new proofs of the Mehler’s formula, the Rogers formula and the generating function for the homogeneous Hahn polynomials Φ(α)n(x,y|q)) by making use of the Cauchy operator and its properties. In addition, some interesting results are also obtained, which include a formal extension of the generating function for Φ(α)n(x,y|q)). VL - 9 IS - 3 ER -
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