论文标题
生成lagendre和legendre样多项式的功能
Generating Functions for Lacunary Legendre and Legendre-like Polynomials
论文作者
论文摘要
使用不同性质的操作方法的使用被证明是一个相当强大的工具，可以研究有关Legendre和Legendre样多项式理论的不同问题。我们展示了如何使用链接Hermite和Legendre（如多项式）的众所周知的积分表示以及操作技术的使用，允许在生成函数，重复的非理性函数的重复衍生物等方面衍生新属性。最终，我们将积分转换的方法扩展到具有多个变量的函数，并根据Legendre多项式获得了给定函数的新扩展标准。
The use of operational methods of different nature is shown to be a fairly powerful tool to study different problems regarding the theory of Legendre and Legendre-like polynomials. We show how the use of the well known integral representations linking Hermite and Legendre like polynomials and of operational technique allow the derivation of new properties regarding the generating functions, repeated derivatives of irrational functions and so on. We finally extend the method of the integral transform to functions with more than one variable and derive new expansion criteria of a given function in terms of Legendre polynomials.
