复杂特型函数高阶导数与原函数统一性的推广

Generalization of the Unity of the Complicated Special Function's Higher-order Derivation and Primary Function

把文献[1]中所研究的高阶导数与原函数的统一性公式,利用数学归纳法推广到了结构更为复杂的特型函数中,获得了比文献[1]应用更为广泛的结果.研究结果表明:高阶导数与原函数这对互逆运算在一些复杂特型函数中可实现统一;利用该结果仅需通过分析该类复杂特型函数的导数与其自身的结构特征,不需做分析运算,即可快速的获得用同一个公式表示该类复杂特型函数的高阶导数与原函数的结果.

Utilization of mathematical induction extends the unity of the higher - order derivation and primary function formula in document [ 1 ] to the special functions whose structural features are more complicated. The results we obtain are more wid - ranging than the ones in document [ 1 ]. The results show that the higher - order derivative and its primary function, the two - way transformer counterparts, can be practically unified in a kind of complicated special functions, and that only through analyzing the structural features of this kind of complicated special functions derivative and those of this kind functions themselves can we obtain quickly the results of the unity of this kind of complicated functions higher- order derivative and their primary functions, without any analysis and operation.