In this paper,we establish two transformation formulas for nonterminating basic hypergeometric series by using Carlitz's inversions formulas and Jackson s transformation formula.In terms of application,by speciali...In this paper,we establish two transformation formulas for nonterminating basic hypergeometric series by using Carlitz's inversions formulas and Jackson s transformation formula.In terms of application,by specializing certain parameters in the two transformations,four Rogers-Ramanujan type identities associated with moduli 20 are obtained.展开更多
In this paper, we derive an elementary identity for smooth solutions of the following equation:$$\Delta u\left( x \right) + K\left( x \right)e^{2u\left( x \right)} = 0\,{\rm in}\,R^2 $$and use it to get some global pr...In this paper, we derive an elementary identity for smooth solutions of the following equation:$$\Delta u\left( x \right) + K\left( x \right)e^{2u\left( x \right)} = 0\,{\rm in}\,R^2 $$and use it to get some global properties of the solutions.展开更多
基金supported by the National Natural Science Foundation of China(12271234)。
文摘In this paper,we establish two transformation formulas for nonterminating basic hypergeometric series by using Carlitz's inversions formulas and Jackson s transformation formula.In terms of application,by specializing certain parameters in the two transformations,four Rogers-Ramanujan type identities associated with moduli 20 are obtained.
文摘In this paper, we derive an elementary identity for smooth solutions of the following equation:$$\Delta u\left( x \right) + K\left( x \right)e^{2u\left( x \right)} = 0\,{\rm in}\,R^2 $$and use it to get some global properties of the solutions.
