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A convenient graphical algorithm for searching and constructing explicit analytical representations of all hypergeometric series belonging to any given class is proposed. The algorithm is based on a set of rules that define a one-to-one correspondence between analytic representations of series and diagrams. The algorithm can be easily implemented in the form of a computer program. 相似文献
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Simultaneous use of general and special linear transformations allows 36 transformations for the Appel function F
4 to be obtained. This result is important because F
4 is widely used in physics and mathematics. The transformations express F
4 in terms of the Appel functions F
1, F
2, and F
3; the Horn function H
2; and non-Hornian series G, K, and . Until now, it was not possible to obtain linear multiplets having such a large dimensionality. A program based on Maple V4 was developed for formula generation. Details of program operation and possible applications of the results obtained are discussed. 相似文献
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A. V. Niukkanen 《Programming and Computer Software》2000,26(2):104-106
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. 相似文献
5.
A Maple-implementation of algorithms for the automatic derivation of hypergeometric series reduction formulas of the most
general form is considered. The list of elementary reductions is presented. 相似文献
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