The identities between the symmetric polynomials
and the sums of
th powers of their variables
![S_k(x_1,...,x_n)=sum_(j=1)^nx_j^k.](/images/equations/Newton-GirardFormulas/NumberedEquation1.svg) |
(1)
|
The identities are given by
![(-1)^mmPi_m(x_1,...,x_n)+sum_(k=1)^m(-1)^(k+m)S_k(x_1,...,x_n)Pi_(m-k)(x_1,...,x_n)=0](/images/equations/Newton-GirardFormulas/NumberedEquation2.svg) |
(2)
|
for each
and for an arbitrary number of variables
. The first few identities are
See also
Power Sum,
Symmetric
Polynomial
Explore with Wolfram|Alpha
References
Séroul, R. "Newton-Girard Formulas." §10.12 in Programming
for Mathematicians. Berlin: Springer-Verlag, pp. 278-279, 2000.Referenced
on Wolfram|Alpha
Newton-Girard Formulas
Cite this as:
Weisstein, Eric W. "Newton-Girard Formulas."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Newton-GirardFormulas.html
Subject classifications