Hypergeometric type q-difference equations: Rodrigues type representation for the second kind solution

Authors:
I. Area;E. Godoy;A. Ronveaux;A. Zarzo
Affiliations:
Departamento de Matemática Aplicada II, E.T.S.E. Telecomunicación, Universidad de Vigo, Vigo 36200, Spain;Departamento de Matemática Aplicada II, E.T.S. Ingenieros Industriales, Universidad de Vigo, Vigo 36200, Spain;Department of Mathematics, Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium;Instituto Carlos I de Fisica Teórica y Computacional, Facultad de Ciencias, Universidad de Granada, Granada, Spain and Departamento de Matemática Aplicada, E.T.S. Ingenieros Industriales ...
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

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Abstract

A Rodrigues type representation for the second kind solution of a second-order q-difference equation of hypergeometric type is given. This representation contains some q-extensions of integrals related with relevant special functions. For these integrals, a general recurrence relation, which only involves the coefficients of the q-difference equation, is also presented.