清代无穷级数研究中的一个关键问题

A KEY PROBLEM IN THE STUDY OF INFINITE SERIES IN THE QING DYNASTY

清初蒙古族数学家明安图创用三种方法,成功地解决了二项式平方根(1—x^2)~1/2的展开问题。这是他推导三角函数幂级数展开式的第一步,也是关键的一步。这一重要贡献足可与著名的'明氏九术'相媲美。

Ming Antu, an eighteenth century Mongolian mathematician of the Qing Dynasty, did profound research on the expansion of trigonometric and anti-trigonometric functions. Besides his proving of the well-known 'Ming's Nine Formulae', he was also a pioneer in his days in tackling the expansion of the binomial squareroot (1-x^2)1/2.The expansion is a crucial step in expanding the sine function into power series.Ming Antu deduced it in three ways. His creative work in deepening the knowledge of the finite and the infinite, which marks a leap-forward from the constant to the variable and from the elementary to higher mathematics, led traditional Chinese mathematics into the new era of Descartes, Newton and Leibniz.