超几何型的升、降算子、因子分解和微分/差分算子
Raising and lowering operators, factorization and differential/difference operators of hypergeometric type
摘要：
本文从Rodrigues公式出发，给出了均匀格上连续变量和离散变量正交多项式的升降算子的一般构造。为了使这些算子相互伴随，我们引入了关于单位权标量积的正交函数。利用Infeld-Hull分解方法，从升、降算子生成了超几何型的二阶自伴微分/差分算子.
英文摘要：
Starting from Rodrigues formula we present a general construction of raising and lowering operators for orthogonal polynomials of continuous and discrete variable on uniform lattice. In order to have these operators mutually adjoint we introduce orthonormal functions with respect to the scalar product of unit weight. Using the Infeld-Hull factorization method, we generate from the raising and lowering operators the second order self-adjoint differential/difference operator of hypergeometric type.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
