两对加权Stirling数偶及其性质

On two weighted Stirling type pairs

从非中心变步长差分与正常差分之间的转换关系出发，导出两对加权型Ｓｔｉｒｌｉｎｇ数偶并讨论了它们的性质．所得结果是Ｃａｒｌｉｔｚ及Ｈｏｗａｒｄ分别讨论的退化Ｓｔｉｒｌｉｎｇ数的直交扩展。

Two weighted Stirling type pairs are derived via the transformations of coefficients between different kinds of non central finite differences with given increments. A quasi Schlmilch formula is proved. The results are orthogonal extensions of the previous results by Howard and Carlitz.