“Newton's Relations”的概念、定义、习题解题方法及翻译-数学辞典

单词

Newton's Relations

释义

Newton's Relations

Let be the sum of the products of distinct Roots of the Polynomial equation of degree

(1)

where the roots are taken

at a time (i.e.,

is defined as the Elementary Symmetric Function

)

is defined for

, ...,

. For example, the first few values of

are

and so on. Then

(5)

This can be seen for a second Degree Polynomialby multiplying out,

(6)

			(7)
			(8)

and for a third Degree Polynomial,


	(9)

See also Elementary Symmetric Function

References

Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, pp. 1-2, 1959.

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。