论文标题
lauricella $ f_d $函数和对称多项式的线性关系
Linear relations for Lauricella $F_D$ functions and symmetric polynomial
论文作者
论文摘要
在本文中，我们开发了一种算法，用于在lauricella $ f_d $函数中获得一些新的线性关系。我们获得的关系，概括了在B. C. Carlson的工作中暗示的关系。这些关系的系数包含在变量中的多项式环中$ x_1，\ dots，x_n $或在某些特殊情况下，在有理函数领域$ {\ mathbb r}（x_1，\ dots，\ dots，x_n，p）$。该方法基于表达适当选择的Euler类型的不确定积分，与这些功能相关联，作为其他Euler型积分和基本功能的线性组合，然后在间隔$ [0,1]上集成。$我们描述了完整的算法以获得这些关系。我们认为，这种关系在计算中可能很有用。
In this paper we develop an algorithm for obtaining some new linear relations among the Lauricella $F_D$ functions. Relations we obtain, generalize those hinted in the work of B. C. Carlson. The coefficients of these relations are contained in the ring of polynomials in the variables $x_1,\dots,x_N$ or in some exceptional cases in the field of rational functions ${\mathbb R}(x_1,\dots,x_N,p)$. The method is based on expressing suitably chosen Euler type indefinite integrals associated with these functions recursively as linear combination of some other Euler type integrals and elementary functions and then integrating over the interval $[0,1].$ We describe the complete algorithm for obtaining these relations. We believe that such relations might be useful in computations.
