کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4642836 | 1341358 | 2007 | 22 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Symmetry groups of Bailey's transformations for 10Ï9-series
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
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چکیده انگلیسی
Although most of the symmetry groups or “invariance groups” associated with two term transformations between (basic) hypergeometric series have been studied and identified, this is not the case for the most general transformation formulae in the theory of basic hypergeometric series, namely Bailey's transformations for Ï910-series. First, we show that the invariance group for both Bailey's two term transformations for terminating Ï910-series and Bailey's four term transformations for non-terminating Ï910-series (rewritten as a two term transformation of a so-called Φ-series) is isomorphic to the Weyl group of type E6. We continue our recent research concerning the group structure underlying three term transformations [S. Lievens, J. Van der Jeugt, Invariance groups of three term transformations for basic hypergeometric series, J. Comput. Appl. Math. 197 (2006) 1-14] and demonstrate that the group associated with a three term transformation between these Φ-series, each admitting Bailey's two term transformation, is the Weyl group of type E7. We do this by giving a description of the root system of type E7 that allows to find a transformation between equivalent three term identities in an easy way. A computation shows that there are five, essentially different, three term transformations between these Φ-series; we give an explicit form of each of these five transformations in an elegant way. To our knowledge only one of these transformations has appeared in the literature.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 206, Issue 1, 1 September 2007, Pages 498-519
Journal: Journal of Computational and Applied Mathematics - Volume 206, Issue 1, 1 September 2007, Pages 498-519
نویسندگان
S. Lievens, J. Van der Jeugt,