The importance of basic hypergeometric series has been widely recognized. For non specialists, it is necessary to have a quick introduction to this classical but flourishing subject. An effort along this direction wil...The importance of basic hypergeometric series has been widely recognized. For non specialists, it is necessary to have a quick introduction to this classical but flourishing subject. An effort along this direction will be made in the present article.展开更多
The purpose of this paper is to establish several transformation formulae for bivariate basic hypergeometric series by means of series rearrangement technique. From these transformations, some interesting summation fo...The purpose of this paper is to establish several transformation formulae for bivariate basic hypergeometric series by means of series rearrangement technique. From these transformations, some interesting summation formulae are obtained.展开更多
The partial sums of basic hypergeometric series are investigated by means of the modified Abel lemma on summation by parts. Several transformation and summation formulae for well-poised, quadratic, cubic and quartic q...The partial sums of basic hypergeometric series are investigated by means of the modified Abel lemma on summation by parts. Several transformation and summation formulae for well-poised, quadratic, cubic and quartic q-series are established.展开更多
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 hy...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.展开更多
文摘The importance of basic hypergeometric series has been widely recognized. For non specialists, it is necessary to have a quick introduction to this classical but flourishing subject. An effort along this direction will be made in the present article.
基金the National Natural Science Foundation of China (No.10771093) the Natural Science Foundation of the Education Department of Henan Province (No.2007110025)
文摘The purpose of this paper is to establish several transformation formulae for bivariate basic hypergeometric series by means of series rearrangement technique. From these transformations, some interesting summation formulae are obtained.
基金supported by National Natural Science Foundation for the Youth (Grant No. 10801026)
文摘The partial sums of basic hypergeometric series are investigated by means of the modified Abel lemma on summation by parts. Several transformation and summation formulae for well-poised, quadratic, cubic and quartic q-series are established.
文摘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.
