A q-analogy of a nonterminating 7F6-series summation
-
摘要: 利用"带余项的"Abel分部求和引理建立一个基本超几何级数变换,其可以看作一个已知非终止三次7F6-级数求和公式的q-模拟.
-
关键词:
- 基本超几何级数 /
- 一般超几何级数 /
- 三次超几何级数 /
- Abel分部求和引理
Abstract: The modified Abel lemma on summation by parts with a "remainder term" was employed to establish a nonterminating basic hypergeometric series transformation which can be seen as a q-analogy of a known 7F6-series summation formula. -
[1] ANDREWS G E, ASKEY R, ROY R. Special Functions[M]. Cambridge:Cambridge University Press, 2000. [2] BAILEY W N. Generalized Hypergeometric Series[M]. Cambridge:Cambridge University Press, 1935. [3] SLATER L J. Generalized Hypergeometric Functions[M]. Cambridge:Cambridge University Press, 1966. [4] GASPER G, RAHMAN M. Basic Hypergeometric Series[M]. 2nd ed. Cambridge:Cambridge University Press, 2004. [5] CHU W. Inversion techniques and combinatorial identity:A unified treatment for the 7F6-series identities[J]. Collect Math, 1994, 45:13-43. [6] CHU W, WANG X Y. Abel's lemma on summation by parts and terminating q-series identities[J]. Numer Algorithms, 2008, 49(1/4):105-128. http://cn.bing.com/academic/profile?id=8b3b472c1d32774cf048117bb80874af&encoded=0&v=paper_preview&mkt=zh-cn [7] WANG C Y, CHEN X J. New proof for a nonterminating cubic hypergeometric series identity of Gasper-Rahman[J]. Journal of Nanjing University (Mathematical Biquarterly), 2015, 32:38-45. [8] WANG C Y. New transformation for the partial sum of a cubic q-series[J]. Journal of East China Normal University (Natural science), 2015, 6:46-52. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=hdsfdxxb201506007 [9] GESSEL I, STANTON D. Strange evaluations of hypergeometric series[J]. SIAM J Math Anal, 1982, 13:295-308. doi: 10.1137/0513021 [10] GASPER G, RAHMAN M. An indefinite bibasic summation formula and some quadratic, cubic and quartic summation and transformation formulas[J]. Canad J Math, 1990, 42:1-27. doi: 10.4153/CJM-1990-001-5 [11] WANG C Y, DAI J J, MEZÖ I. A nonterminating 7F6-series evaluation[J]. Integral Transforms and Special Functions, 2018, 29(9):719-724. doi: 10.1080/10652469.2018.1492571 [12] BAILEY W N. A note on certain q-identities[J]. Quart J Math (Oxford), 1941, 12:173-175. [13] DAUM J A. The basic analogue of Kummer's theorem[J]. Bull Amer Math Soc, 1942, 48:711-713. doi: 10.1090/S0002-9904-1942-07764-0
点击查看大图
计量
- 文章访问数: 165
- HTML全文浏览量: 112
- PDF下载量: 104
- 被引次数: 0