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math.CA2024
New proofs of theorems on q-orthogonal functions
Dandan Chen, Zhiguo Liu
In this paper, we establish a -integral formula by using the orthogonality relation, and also provide a new proof of the -orthogonality relation for the continuous -ultras…
math.CA2024
A conjecture of Gasper on -ultraspherical polynomials
Dandan Chen, Siyu Yin
In this paper we establish -orthogonality relation for the continuous -ultraspherical polynomials, which was considered by Gasper. Additionally, we evaluate a new -beta in…