清代中算家的递加数

级数论是有清以来传统数学的主流，通过对递加数的研究，可加深了解其中的情节。递加数是清代中后期级数论中的重要内容，清代中算家为此做了大量的工作。该文依据原著，递归地描述其生成模型，在此基础上对递加数进行了比较充分的讨论，表明它是产生于割圆连比例并用以确定一类无穷幂级数展开式系数的一种递归过程，从而试图反映出清代级数论所固的递归特性。

DI JIA SHU IN THE QING DYNASTY

Di Jia Shu is a Chinese creation by which the coefficients for a sort of power series were decided in the middle and late periods of the Qing Dynasty.It is not only a mirror of Chinese mathematicians'simple endeavours to have infinitudes well in hand, but an elementary attempt about the combinational field as well. This paper examines every process of the birth, the growth and the making use of in Jia Shu,and tries to picture it as complete as possible.