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

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Abstract

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.

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Correspondence to A. V. Niukkanen.

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Niukkanen, A.V. New algorithms in the theory of hypergeometric series and Burchnall-Chaundy expansions. Program Comput Soft 26, 104–106 (2000). https://doi.org/10.1007/BF02759197

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  • DOI: https://doi.org/10.1007/BF02759197

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