New proofs of theorems on q-orthogonal functions
Abstract
In this paper, we establish a $q$-integral formula by using the orthogonality relation, and also provide a new proof of the $q$-orthogonality relation for the continuous $q$-ultraspherical polynomials. A new $q$-beta integral with five parameters is evaluated.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.04444
- arXiv:
- arXiv:2408.04444
- Bibcode:
- 2024arXiv240804444C
- Keywords:
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- Mathematics - Classical Analysis and ODEs;
- Mathematics - Number Theory