A Formula Containing Four Independent Bases and Its Applications
一个含四个独立基的变换公式及其应用(英文)
摘要
A transformation formula containing four independent bases is found by a special inversion formula and it is applied to derive a few summation formulas for basic hypergeometric series only by elementary method. The hypergeometric series, the limits of those formulas are also obtained.
本文利用反演的方法得到了一个四个独立基的变换公式并由此得到了几个新的基本超几何级数求和公式和超几何级数求和公式.
参考文献4
-
1GASPER G. Summation,transformation and expansion formulas for bibasle series [J]. Trans. Amer. Math. Soc., 1989, 312: 257-277.
-
2GASPER 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.
-
3GASPER G, RAHMAN M. Basic Hypergeometric Series [M]. Encyclopedia Math. Appl., Vol. 35, Cambridge Univ. Press, Cambridge, 1990.
-
4ZHANG Yu-sen, WANG Tian-ming. Some applications of Gasper's bibasic summation formula [J], Indian J. Pure & Appl. Math., to appear.
-
1及万会,张来萍.寻求组合恒等式[J].河南教育学院学报（自然科学版）,2008,17(2):19-21. 被引量：1
-
2陶长琪,徐晔.一类基本超几何级数的估计[J].商丘师专学报,2000,16(2):50-53. 被引量：3
-
3袁平之.关于丢番图方程x^2=4p^m+4p^n+1[J].岳阳大学学报,1995,11(1):13-17.
-
4蔡懿.关于q-二项式系数的有关性质和等式[J].周口师范学院学报,2013,30(5):11-13.
-
5陶长琪.基本超几何级数求和的一个注记[J].江西师范大学学报（自然科学版）,1999,23(1):75-77. 被引量：4
-
6陈宝振,陈鹏.超几何级数余项估计[J].计算物理,1992,9(A01):546-546.
-
7陶长琪,刘满凤.基本超几何级数的几个估计[J].南昌大学学报（理科版）,1999,23(1):26-28. 被引量：2
-
8初文昌,徐利治.关于组合和的超几何级数方法[J].高校应用数学学报（A辑）,1990,5(1):125-136.
-
9刘红梅,周文书,李阳.双变量超几何级数的变换与简化公式[J].数学物理学报（A辑）,2016,36(1):150-156.
-
10Hongmei LIU,Shuyan DING,Shuhua QI.Gould-Hsu Inversion Chains and Their Applications[J].Journal of Mathematical Research with Applications,2012,32(2):167-173.
