A set of generalized symmetries with arbitrary functions of t for the Konopelchenko-Dubrovsky (KD)equation in 2+1 space dimensions is given by using a direct method called formal function series method presented by Lo...A set of generalized symmetries with arbitrary functions of t for the Konopelchenko-Dubrovsky (KD)equation in 2+1 space dimensions is given by using a direct method called formal function series method presented by Lou. These symmetries constitute an infinite-dimensional generalized w∞ algebra.展开更多
In this paper, we studies the relations between the mean value and the maximun norm of the infinite order entire functions which defined by legendre series. We obtained that if f(z) is an infinite order entire functio...In this paper, we studies the relations between the mean value and the maximun norm of the infinite order entire functions which defined by legendre series. We obtained that if f(z) is an infinite order entire function with a positive exponenatial lower order. then loaM (α) ～logMδ(α) ～ logMδ(α) (α→+∞).展开更多
Here is introduced some novel algorithms which made use of polygarnma functions to get the exact limits of a broad class of infinite series. Moreover, Laplace transform is used to find the sum of many convergent infin...Here is introduced some novel algorithms which made use of polygarnma functions to get the exact limits of a broad class of infinite series. Moreover, Laplace transform is used to find the sum of many convergent infinite series. These exact limits are found in different branches of physics for some special cases series and are in complete agreement with the values found by other authors. Moreover, the methods presented here are generalized and applied to other wide variety of sums, including alternating series. Finally, these methods are simple and quite powerful to calculate the limits of many convergent series as you can see from the examples included.展开更多
基金浙江省自然科学基金，浙江省宁波市博士基金，the State Key Laboratory of Oil/Gas Reservoir Geology and Exploitation，Scientific Research Fund of Education Department of Zhejiang Province under
文摘A set of generalized symmetries with arbitrary functions of t for the Konopelchenko-Dubrovsky (KD)equation in 2+1 space dimensions is given by using a direct method called formal function series method presented by Lou. These symmetries constitute an infinite-dimensional generalized w∞ algebra.
文摘In this paper, we studies the relations between the mean value and the maximun norm of the infinite order entire functions which defined by legendre series. We obtained that if f(z) is an infinite order entire function with a positive exponenatial lower order. then loaM (α) ～logMδ(α) ～ logMδ(α) (α→+∞).
文摘Here is introduced some novel algorithms which made use of polygarnma functions to get the exact limits of a broad class of infinite series. Moreover, Laplace transform is used to find the sum of many convergent infinite series. These exact limits are found in different branches of physics for some special cases series and are in complete agreement with the values found by other authors. Moreover, the methods presented here are generalized and applied to other wide variety of sums, including alternating series. Finally, these methods are simple and quite powerful to calculate the limits of many convergent series as you can see from the examples included.
