Newton's Relations
Let 
be the sum of the products of distinct Roots 
of the Polynomial equation of degree 
 | (1) |
at a time (i.e., is defined as the Elementary Symmetric Function 
) is defined for 
, ..., . For example, the first few values of are |  |  | (2) |
 | |  | (3) |
 | |  | (4) |
and so on. Then
 | (5) |
 | (6) |
| |  | (7) |
| |  | (8) |
and for a third Degree Polynomial,
 | |
 | (9) |
| |  | (10) |
| |  | (11) |
| |  | (12) |
See also Elementary Symmetric Function
References
Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, pp. 1-2, 1959.
- Radon Transform--Square
- Rado's Sigma Function
- Railroad Track Problem
- Ramanujan 6-10-8 Identity
- Ramanujan Constant
- Ramanujan Continued Fraction
- Ramanujan Cos/Cosh Identity
- Ramanujan-Eisenstein Series
- Ramanujan Function
- Ramanujan g- and G-Functions
- Ramanujan-Petersson Conjecture
- Ramanujan Psi Sum
- Ramanujan's Hypergeometric Identity
- Ramanujan's Hypothesis
- Ramanujan's Identity
- Ramanujan's Integral
- Ramanujan's Interpolation Formula
- Ramanujan's Master Theorem
- Ramanujan's Square Equation
- Ramanujan's Sum
- Ramanujan's Sum Identity
- Ramanujan's Tau-Dirichlet Series
- Ramanujan's Tau Function
- Ramanujan Theta Functions
- Ramp Function