论文标题
超几何序列的差分差异特性
Differential-Difference Properties of Hypergeometric Series
论文作者
论文摘要
在可变$ x $中的六个广义高几何序列的家庭，并考虑了任意数量的参数。他们每个人都由整数$ n $索引。 $ n $中的线性复发关系通过可变$ x $将这些功能及其产品联系起来。我们将这些方程式的明确分解为一阶复发操作员的产品。相关复发也是针对$ x $的导数得出的。这些公式概括了经典正交多项式的众所周知的特性。
Six families of generalized hypergeometric series in a variable $x$ and an arbitrary number of parameters are considered. Each of them is indexed by an integer $n$. Linear recurrence relations in $n$ relate these functions and their product by the variable $x$. We give explicit factorizations of these equations as products of first order recurrence operators. Related recurrences are also derived for the derivative with respect to $x$. These formulas generalize well-known properties of the classical orthogonal polynomials.
