Volterra-type convolution of classical polynomials. (English) Zbl 1428.42011
the authors presented a general framework for calculating the Volterra-type convolution of polynomials from an arbitrary polynomial sequence \(\{P_k(x)\}\) \(k \geq 0\) with deg \(P_k(x) = k.\) Based on this framework, series representations for the convolutions of classical orthogonal polynomials, including Jacobi and Laguerre families, are derived.
Reviewer: Ilia V. Boikov (Penza)
MSC:
| 42A85 | Convolution, factorization for one variable harmonic analysis |
| 44A35 | Convolution as an integral transform |
| 33C05 | Classical hypergeometric functions, \({}_2F_1\) |
| 33C20 | Generalized hypergeometric series, \({}_pF_q\) |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
Keywords:
convolution; Volterra convolution integral; orthogonal polynomials; Jacobi polynomials; Gegenbauer polynomials; Legendre polynomials; Chebyshev polynomials; Laguerre polynomialsSoftware:
DLMFReferences:
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