A characterization of continuous q-Jacobi, Chebyshev of the first kind and Al-Salam Chihara polynomials
K. Castillo, D. Mbouna, J. Petronilho
Abstract
The purpose of this note is to characterize those orthogonal polynomials sequences (Pn)n≥0 for whichπ(x)DqPn(x)=(anx+bn)Pn(x)+cnPn−1(x),n=0,1,2,…, where Dq is the Askey-Wilson operator, π is a polynomial of degree at most 2, and (an)n≥0, (bn)n≥0 and (cn)n≥0 are sequences of complex numbers such that cn≠0 for n=1,2,….
Topics & Concepts
MathematicsChebyshev polynomialsOrthogonal polynomialsCharacterization (materials science)Jacobi polynomialsDegree (music)Operator (biology)PolynomialCombinatoricsClassical orthogonal polynomialsDiscrete orthogonal polynomialsGegenbauer polynomialsPure mathematicsDiscrete mathematicsMathematical analysisChemistryPhysicsGeneOpticsAcousticsTranscription factorBiochemistryRepressorMathematical functions and polynomialsAnalytic and geometric function theoryAdvanced Mathematical Identities