Hypergeometric symbolic calculus. II – Systems of confluent equations

We apply the hypergeometric symbolic calculus introduced in the previous work [A. Debiard, B. Gaveau, Hypergeometric symbolic calculus. I – Systems of two symbolic hypergeometric equations] to the determination of the general solution of degenerate hypergeometric equations in two variables and to th...

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Bibliographic Details
Published in:Bulletin des sciences mathématiques 2003-05, Vol.127 (3), p.261-280
Main Authors: Debiard, Amédée, Gaveau, Bernard
Format: Article
Language:English
Subjects:
Appell series
Exact sciences and technology
Horn series
Mathematical analysis
Mathematics
Sciences and techniques of general use
Special functions
Symbolic calculus
Two variables hypergeometric differential operators
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Summary:We apply the hypergeometric symbolic calculus introduced in the previous work [A. Debiard, B. Gaveau, Hypergeometric symbolic calculus. I – Systems of two symbolic hypergeometric equations] to the determination of the general solution of degenerate hypergeometric equations in two variables and to the determination of a basis of the vector space of solutions of the 20 confluent systems of Horn. Nous définissons un nouveau calcul hypergéométrique symbolique qui permet la détermination des solutions générales d'équations aux dérivées partielles hypergéométriques de deux variables. Nous appliquons cette méthode à la détermination d'une base de l'espace vectoriel des solutions des 14 systèmes d'Appell–Kampé de Fériet et Horn. Nous en déduisons ainsi de nouvelles représentations intégrales des solutions.
ISSN:0007-4497
1952-4773
DOI:10.1016/S0007-4497(03)00017-4