caa a22 4500 475741927 CHVBK 20180406123501.0 cr unu---uuuuu 170329e20000401xx s 000 0 eng 10.1007/BF02676405 doi (NATIONALLICENCE)springer-10.1007/BF02676405 Niukkanen A. V. I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, USSR aut Extending the factorization principle to hypergeometric series of general form [Elektronische Daten] [A. Niukkanen] It is shown that the formulas of operator factorization of hypergeometric functions obtained in the author's previous works can be extended to hypergeometric series of the most general form. This generalization does not make the technical apparatus of the factorization method more complicated. As an example illustrating the practical effectiveness of the formulas obtained in the paper, we analyze transformation properties of the Horn seriesG 3, whose structure is typical for general hypergeometric functions. It is shown that Erdélyi's transformation formula relating the seriesG 3 to the Appell functionF 2, contains erroneous expressions in the arguments ofG 3. The correct analog of Erdélyi's formula is found, and some new transformations of the seriesG 3 are presented. Kluwer Academic/Plenum Publishers, 2000 general hypergeometric functions nationallicence transformation formulas nationallicence Horn and Appell functions nationallicence Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/4(2000-04-01), 487-494 0001-4346 67:4<487 2000 67 11006 https://doi.org/10.1007/BF02676405 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02676405 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Niukkanen A. V. I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, USSR aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/4(2000-04-01), 487-494 0001-4346 67:4<487 2000 67 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer