“Newton’s identities”的概念、定义、翻译、参考文献-科学参考

单词	Newton’s identities
释义	Newton’s identities Mathematics Given a polynomial a_nxⁿ+a_n–1x^n–1+ ⋅⋅⋅ +a₀ = 0, let s_k denote the sum of the kth powers of the polynomial’s roots. Then Newton’s identities state for k ≥1 that $a_{n} s_{k} + a_{n - 1} s_{k - 1} + \dots + a_{n - k + 1} s_{1} + k a_{n - k} = 0.$ These identities recursively determine s_k in terms of s_k–1,….,s₁. In these identities a_r is understood to be 0 if r<0. See also elementary symmetric polynomials.
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