Second order q-difference equations solvable by factorization method

2003/12/22 by Alina Dobrogowska, Dobrogowska, Alina, Anatol Odzijewicz +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0312057

21 pages

arxiv created 2003/12/22 · arxiv updated 2009/12/01

Abstract

By solving an infinite nonlinear system of q-difference equations one constructs a chain of q-difference operators. The eigenproblems for the chain are solved and some applications, including the one related to q-Hahn orthogonal polynomials, are discussed. It is shown that in the limit q->1 the present method corresponds to the one developed by Infeld and Hull.

Related

• Factorization method and general second order linear difference equation
• Linear partial q-difference equations on q-linear lattices and their bivariate q-orthogonal polynomial solutions
• Jacobi operator, q-difference equation and orthogonal polynomials
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