New algorithms in the theory of hypergeometric series and Burchnall-Chaundy expansions

It is shown that the Burchnall-Chaundy expansions, which are of fundamental importance in the theory of Appell's functions, can easily be implemented and generalized by means of the operator factorization method, which provides a simple and universal base, both for a new theory of hypergeometri...

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Veröffentlicht in:Programming and computer software 2000-03, Vol.26 (2), p.104-106
1. Verfasser: Niukkanen, A. V.
Format: Artikel
Sprache:eng
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Zusammenfassung:It is shown that the Burchnall-Chaundy expansions, which are of fundamental importance in the theory of Appell's functions, can easily be implemented and generalized by means of the operator factorization method, which provides a simple and universal base, both for a new theory of hypergeometric series and for the development of effective new algorithms for computer-aided symbolic transformations of these series. Five new generalized expansions are derived, including 44 Burchnall-Chaundy expansions, as well as many new expansions, some of which are related to the Horn series.
ISSN:0361-7688
1608-3261
DOI:10.1007/BF02759197