New proofs of theorems on q-orthogonal functions
Dandan Chen, Zhiguo Liu
TL;DR
This paper introduces new proofs for theorems related to q-orthogonal functions, including a q-integral formula, a q-orthogonality relation, and a five-parameter q-beta integral, advancing mathematical understanding of these functions.
Contribution
It provides novel proofs of key properties of q-orthogonal functions, including a new q-integral formula and a q-beta integral with five parameters.
Findings
Established a q-integral formula using orthogonality.
Provided a new proof of the q-orthogonality relation for continuous q-ultraspherical polynomials.
Evaluated a new q-beta integral with five parameters.
Abstract
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 -ultraspherical polynomials. A new -beta integral with five parameters is evaluated.
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Taxonomy
TopicsMathematical functions and polynomials · Advanced Optimization Algorithms Research · Mathematical Inequalities and Applications