Hypergeometric-type differential equations: second kind solutions and related integrals

Authors:
I. Area;E. Godoy;A. Ronveaux;A. Zarzo
Affiliations:
Departamento de Matemática Aplicada II, E.T.S.E. Telecomunicación, Universidade de Vigo, 36200-Vigo, Spain;Departamento de Matemática Aplicada II, E.T.S. Ingenieros Industriales, Universidad de Vigo, 36200-Vigo, Spain;Mathematical Physics, Facultés Universitaires Notre-Dame de la Paix, B-5000 Namur, Belgium;Instituto Carlos I de Física Teórica y Computacional, Facultad de Ciencias, Universidad de Granada, Spain and Departamento de Matemática Aplicada, E.T.S. Ingenieros Industriales, Un ...
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

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Abstract

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