论文标题
部分可观测时空混沌系统的无模型预测
$ε$-Expansion of Multivariable Hypergeometric Functions Appearing in Feynman Integral Calculus
论文作者
论文摘要
我们提出了一种适合在计算机上实现的新方法，可在任何数量的变量中使用线性$ε$依赖性Pochhammer参数执行$ε$ - $ε$扩展。我们的方法允许人们执行泰勒以及多变量超几何功能的劳伦斯系列扩展。串联扩展中$ε$的每个系数均表示为多变量超几何函数的线性组合，具有与原始超几何函数相同的收敛域的线性组合。我们介绍了一个，两个和三个变量中的超几何函数的说明性示例，这些变量是Feynman积分计算的典型示例。
We present a new methodology, suitable for implementation on computer, to perform the $ε$-expansion of hypergeometric functions with linear $ε$ dependent Pochhammer parameters in any number of variables. Our approach allows one to perform Taylor as well as Laurent series expansion of multivariable hypergeometric functions. Each of the coefficients of $ε$ in the series expansion is expressed as a linear combination of multivariable hypergeometric functions with the same domain of convergence as that of the original hypergeometric function. We present illustrative examples of hypergeometric functions in one, two and three variables which are typical of Feynman integral calculus.
